Chapter 12

Class 7 Mathematics · 124 questions · 95 with answers

Solved examples

example-1Multiple choice

Which of the following is not a symmetrical figure?

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Solution: Correct answer is (d).

example-2Multiple choice

In the word “MATHS” which of the following pairs of letters shows rotational symmetry

(a)M and T
(b)H and S
(c)A and S
(d)T and S

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Solution: Correct answer is (b).

example-3Multiple choice

The angle of rotation for the figure 12.2 is

(a)45°
(b)60°
(c)90°
(d)180° Fig. 12.2

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Solution: Correct answer is (C) In Examples 4 to 6, fill in the blanks to make it a true statement.

example-4Fill in the blanks

The figure 12.3 has ________ vertices, __________ edges and __________ faces.

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Solution: 10, 15, 7 Fig. 12.3 15-04-2018

example-5Fill in the blanks

The adjoining net in Fig. 12.4 represents a _________.

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Solution: Cube

example-6Fill in the blanks

Rotation turns an object about a fixed point. This fixed point is called _______.

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Solution: centre of rotation. Fig. 12.4 In Examples 7 to 9, state whether the statements are True or False.

example-7Short answer

A net of a 3-D shape is a sort of skeleton - outline in 2-D, which, when folded results in the 3-D shape.

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Solution: True

example-8Short answer

A regular pentagon has no lines of symmetry.

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Solution: False Translation Rotation Reflection A translation slides A rotation turns a A reflection flips a a figure along the figure around a figure across a line direction of a line point, called the to create a mirror without turning. centre of rotation. image.

example-9Short answer

Order of rotational symmetry for the figure 12.5 is 4. Fig. 12.5

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Solution: False 15-04-2018

example-10Short answer

Draw all the lines of symmetry for the following letters if they exist. Solution

example-11Short answer

State whether the figure 12.6 shows rotational symmetry. If yes, then what is the order of rotational symmetry?

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Solution: The given figure shows rotational symmetry. The order of symmetry = 4, Fig. 12.6 which is clear from the following figure: Note: The dot is placed just to indentify different positions of the figure.

example-12Multiple choice

Identify the following figures:

(i)
(ii)Fig. 12.7 15-04-2018

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Solution: (i) Rectangular Pyramid (ii) Triangular Prism

example-13Multiple choice

Construct a triangle PQR such that PQ = 6 cm, QR = 7 cm and PR = 4.5 cm. Solution Steps:

(i)Draw a line segment PQ of length 6 cm.
(ii)With P as centre, draw an arc of radius 4.5 cm.
(iii)With Q as centre, draw an arc of radius 7 cm which intersects the previous arc at R.
(iv)Join PR and QR. Then ∆PQR is the required triangle (Fig. 12.8). Fig. 12.8

example-14Short answer

Draw the top, the front and the side views of the following solid figure made up of cubes. Fig. 12.9 15-04-2018

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Solution: Desired views are shown in Fig. 12.10 below Fig. 12.10 Nature provides many beautiful examples of symmetry, such as the wings of a butterfly and a peacock or the petals of a flower. Symmetric objects have parts that are congruent. A figure has line symmetry if you can draw a line through it so that the two sides are mirror images of each other. The line is called the line of symmetry.

example-15Multiple choice

Given a line l and a point M on it draw a perpendicular MP to l where MP = 5.2cm and a line q parallel to l through P. 15-04-2018 Solution Fig. 12.11 Steps :

(i)Draw a line l .
(ii)Take a point M on it.
(iii)Draw an angle of 90° at M with l which is perpendicular to l at M.
(iv)With M as centre and radius 5.2 cm, draw an arc which intersects the above perpendicular at point P. MP is the required prependicular (v) At P, draw an angle of 90° with PM and produce to make a line q. Line q is the required line parallel to line l.

example-16Short answer

Determine the number of edges, vertices and faces in the Fig. 12.12. Fig. 12.12

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Solution: Understand and Explore the Problem 15-04-2018 • What information is given in the question? A square pyramid. • What are you trying to find? The number of edges. vertices and faces. • Is there any information that is not needed? The measure of the edges are not needed. Plan a Strategy • Recall the definitions of edges, vertices and faces of a 3-D figure and try to co-relate them to the figure given above. Solve • The different plain regions are called faces. Hence, there are 5 faces. • The line segments formed, where the faces meet are called edges. Hence, there are 8 edges. • Edges meet at a point which are called vertices. Hence, there are 5 vertices. • Therefore, a square pyramid has 5 faces, 5 vertices and 8 edges. Revise • Try to find the number of vertices and edges of a cuboid. Can you see a pattern emerging based on your findings? you can observe that F+V=E+2 Where F,V,E denote number of faces, number of vertices and number of edges respectively of such solids. This is known as ‘EULER’s FORMULA’. You’ll study this concept in your next class. Try to find the number of edges, vertices and faces in some more solids and explore the pattern, if any. 15-04-2018 A figure has rotational symmetry if you can rotate the figure around some point so that it coincides with itself. The point is the centre of rotation, and the amount of rotation must be less than one full turn, or 360°. 7-fold and 6-fold rotational symmetry mean that the figures coincide with themselves 7 times and 6 times respectively, within one full turn. 7-fold rotational symmetry 6-fold rotational symmetry In each of the Questions 1 to 26, there are four options, out of which one is correct. Choose the correct one.

Questions

Q1Multiple choice

A triangle can be constructed by taking its sides as:

(a)1.8 cm, 2.6 cm, 4.4 cm
(b)2 cm, 3 cm, 4 cm
(c)2.4 cm, 2.4 cm, 6.4 cm
(d)3.2 cm, 2.3 cm, 5.5 cm

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Across 6.

Q2Multiple choice

A triangle can be constructed by taking two of its angles as:

(a)110°, 40°
(b)70°, 115°
(c)135°, 45°
(d)90°, 90°

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Q3Multiple choice

The number of lines of symmetry in the figure given below is:

This question refers to a figure in the original PDF.

(a)4
(b)8
(c)6
(d)Infinitely many Fig. 12.13 15-04-2018 1. Explain what it means for a figure to be symmetric. 2. Tell which capital letters of the alphabet have line symmetry. 3. Tell which capital letters of the alphabet have rotational symmetry.

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Q4Multiple choice

The number of lines of symmetry in Fig. 12.14 is

This question refers to a figure in the original PDF.

(a)1
(b)3
(c)6
(d)Infinitely many

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Q5Multiple choice

The order of rotational symmetry in the Fig. 12.15 Fig. 12.14 given below is

This question refers to a figure in the original PDF.

(a)4
(b)8
(c)6
(d)Infinitely many Fig. 12.15

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(b) 8

(a) 4

Q6Multiple choice

The order of rotational symmetry in the figure 12.16 given below is

This question refers to a figure in the original PDF.

(a)4
(b)2 Fig. 12.16
(c)1
(d)Infinitely many

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(b) 2 Fig. 12.16

Q7Multiple choice

The name of the given solid in Fig 12.17 is:

This question refers to a figure in the original PDF.

(a)triangular pyramid
(b)rectangular pyramid
(c)rectangular prism
(d)triangular prism Fig. 12.17 15-04-2018 1. Give a situation in which the front and side views of a figure would be the same. 2. Explain whether it is possible for all of the views of a figure to be congruent rectangles.

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(b) rectangular pyramid

Q8Multiple choice

The name of the solid in Fig. 12.18 is:

This question refers to a figure in the original PDF.

(a)triangular pyramid
(b)rectangular prism
(c)triangular prism
(d)rectangular pyramid

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Q9Multiple choice

All faces of a pyramid are always: Fig. 12.18

This question refers to a figure in the original PDF.

(a)Triangular
(b)Rectangular
(c)Congruent
(d)None of these

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(d) None of these

Q10Multiple choice

A solid that has only one vertex is

(a)Pyramid
(b)Cube
(c)Cone
(d)Cylinder

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Q11Multiple choice

Out of the following which is a 3-D figure?

(a)Square
(b)Sphere
(c)Triangle
(d)Circle

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(b) Sphere

Q12Multiple choice

Total number of edges a cylinder has

(a)0
(b)1
(c)2
(d)3

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Q13Multiple choice

A solid that has two opposite identical faces and other faces as parallelograms is a

(a)prism
(b)pyramid
(c)cone
(d)sphere

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(a) prism

Q14Multiple choice

The solid with one circular face, one curved surface and one vertex is known as:

(a)cone
(b)sphere
(c)cylinder
(d)prism

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(a) cone

Q15Multiple choice

If three cubes each of edge 4 cm are placed end to end, then the dimensions of resulting solid are:

(a)12 cm × 4 cm × 4 cm
(b)4 cm × 8 cm × 4 cm
(c)4 cm × 8 cm × 12 cm
(d)4 cm × 6 cm × 8 cm 15-04-2018

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(a) 12 cm × 4 cm × 4 cm

Q16Multiple choice

When we cut a corner of a cube as shown in the figure 12.19, we get the cutout piece as :

This question refers to a figure in the original PDF.

(a)square pyramid
(b)trapezium prism
(c)triangular pyramid
(d)a triangle Fig. 12.19

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Q17Multiple choice

If we rotate a right-angled triangle of height 5 cm and base 3 cm about its height a full turn, we get

(a)cone of height 5 cm, base 3 cm
(b)triangle of height 5 cm, base 3 cm
(c)cone of height 5 cm, base 6 cm
(d)triangle of height 5 cm, base 6 cm

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(a) cone of height 5 cm, base 3 cm

Q18Multiple choice

If we rotate a right-angled triangle of height 5 cm and base 3 cm about its base, we get:

(a)cone of height 3 cm and base 3 cm
(b)cone of height 5 cm and base 5 cm
(c)cone of height 5 cm and base 3 cm
(d)cone of height 3 cm and base 5 cm

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(d) cone of height 3 cm and base 5 cm

Q19Multiple choice

When a torch is pointed towards one of the vertical edges of a cube, you get a shadow of cube in the shape of

(a)square
(b)rectangle but not a square
(c)circle
(d)triangle

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(b) rectangle but not a square

Q20Multiple choice

Which of the following sets of triangles could be the lengths of the sides of a right-angled triangle:

(a)3 cm, 4 cm, 6 cm
(b)9 cm, 16 cm, 26 cm
(c)1.5 cm, 3.6 cm, 3.9 cm
(d)7 cm, 24 cm, 26 cm 15-04-2018

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Q21Multiple choice

In which of the following cases, a unique triangle can be drawn

(a)AB = 4 cm, BC = 8 cm and CA = 2 cm
(b)BC = 5.2 cm, ∠B = 90° and ∠C = 110°
(c)XY = 5 cm, ∠X = 45° and ∠Y = 60°
(d)An isosceles triangle with the length of each equal side 6.2 cm.

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Q22Multiple choice

Which of the following has a line of symmetry ?

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(c)

Q23Multiple choice

Which of the following are reflections of each other?

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(a)

Q24Multiple choice

Which of these nets is a net of a cube?

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(b)

Q25Multiple choice

Which of the following nets is a net of a cylinder ?

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(c)

Q26Multiple choice

Which of the following letters of English alphabets have more than 2 lines of symmetry?

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(b)

Q27Multiple choice

Take a square piece of paper as shown in figure (1). Fold it along its diagonals as shown in figure (2). Again fold it as shown in figure (3). Imagine that you have cut off 3 pieces of the form of congruent 15-04-2018 isosceles right-angled triangles out of it as shown in figure 4. (1) (2) (3) (4) On opening the piece of paper which of the following shapes will you get?

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(a)

Q28Multiple choice

Which of the following 3-dimensional figures has the top, side and front as triangles?

(a)
(b)
(c)
(d)In Questions 29 to 58, fill in the blanks to make the statements true.

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(c)

Q29Fill in the blanks

In an isosceles right triangle, the number of lines of symmetry is ________.

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one

Q30Fill in the blanks

Rhombus is a figure that has ______lines of symmetry and has a rotational symmetry of order _______.

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2,2

Q31Fill in the blanks

__________ triangle is a figure that has a line of symmetry but lacks rotational symmetry.

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Isosceles

Q32Fill in the blanks

__________ is a figure that has neither a line of symmetry nor a rotational symmetry. 15-04-2018

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Quadrilateral

Q33Fill in the blanks

__________ and __________ are the capital letters of English alphabets that have one line of symmetry but they interchange to each other when rotated through 180°.

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M and W

Q34Fill in the blanks

The common portion of two adjacent faces of a cuboid is called __________.

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Edge

Q35Fill in the blanks

A plane surface of a solid enclosed by edges is called __________ .

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Face

Q36Fill in the blanks

The corners of solid shapes are called its __________.

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Vertices

Q37Fill in the blanks

A solid with no vertex is __________.

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Sphere

Q38Fill in the blanks

A triangular prism has __________ faces, __________ edges and __________ vertices.

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5, 9, 6

Q39Fill in the blanks

A triangular pyramid has __________ faces, __________ edges and __________vertices.

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4, 6, 4

Q40Fill in the blanks

A square pyramid has __________ faces, __________ edges and __________ vertices.

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5, 8, 5

Q41Fill in the blanks

Out of __________ faces of a triangular prism, __________are rectangles and __________ are triangles.

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5, 3, 2

Q42Fill in the blanks

The base of a triangular pyramid is a __________.

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Triangle

Q43Fill in the blanks

Out of __________ faces of a square pyramid, __________ are triangles and __________ is/are squares.

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5, 4, 1

Q44Fill in the blanks

Out of __________ faces of a rectangular pyramid __________ are triangles and base is __________.

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5, 4, rectangle

Q45Fill in the blanks

Each of the letters H, N, S and Z has a rotational symmetry of order __________.

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Q46Fill in the blanks

Order of rotational symmetry of a rectangle is __________.

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Q47Fill in the blanks

Order of rotational symmetry of a circle is __________.

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Infinite

Q48Fill in the blanks

Each face of a cuboid is a __________.

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Rectangle

Q49Fill in the blanks

Line of symmetry for an angle is its __________.

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Bisector

Q50Fill in the blanks

A parallelogram has __________ line of symmetry. 15-04-2018

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Q51Fill in the blanks

Order of rotational symmetry of is _________.

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Q52Fill in the blanks

A __________ triangle has no lines of symmetry.

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Scalene

Q53Fill in the blanks

Cuboid is a rectangular_________ .

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Prism

Q54Fill in the blanks

A sphere has __________vertex, __________edge and __________curved surface.

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0, 0, 1

Q55Fill in the blanks

is a net of a __________. → Circumference of circle = ______.

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Cone

Q56Fill in the blanks

is a net of a __________.

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Triangle Prism

Q57Fill in the blanks

Order of rotational symmetry of is __________.

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Q58Fill in the blanks

Identical cubes are stacked in the corner of a room as shown below. The number of cubes that are not visible are _________. Fig. 12.20 15-04-2018 In Questions from 59 to 92, state whether the statements are True or False.

This question refers to a figure in the original PDF.

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Q59Short answer

We can draw exactly one triangle whose angles are 70°, 30° and 80°.

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False

Q60Short answer

The distance between the two parallel lines is the same everywhere.

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True

Q61Short answer

A circle has two lines of symmetry.

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False

Q62Short answer

An angle has two lines of symmetry.

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False

Q63Short answer

A regular hexagon has six lines of symmetry.

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True

Q64Short answer

An isosceles trapezium has one line of symmetry.

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True

Q65Short answer

A parallelogram has two lines of symmetry.

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False

Q66Short answer

Order of rotational symmetry of a rhombus is four.

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False

Q67Short answer

An equilateral triangle has six lines of symmetry.

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False

Q68Short answer

Order of rotational symmetry of a semi circle is two.

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False

Q69Short answer

In oblique sketch of the solid, the measurements are kept propor- tional.

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False

Q70Short answer

An isometric sketch does not have proportional length.

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False

Q71Short answer

A cylinder has no vertex.

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True

Q72Short answer

All the faces, except the base of a square pyramid are triangular.

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True

Q73Short answer

A pyramid has only one vertex.

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False

Q74Short answer

A triangular prism has 5 faces, 9 edges and 6 vertices.

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True

Q75Short answer

If the base of a pyramid is a square, it is called a square pyramid.

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True

Q76Short answer

A rectangular pyramid has 5 rectangular faces.

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False

Q77Short answer

Rectangular prism and cuboid refer to the same solid.

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True

Q78Short answer

A tetrahedron has 3 triangular faces and 1 rectangular face.

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False

Q79Short answer

While rectangle is a 2-D figure, cuboid is a 3-D figure.

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True

Q80Short answer

While sphere is a 2-D figure, circle is a 3-D figure.

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False

Q81Short answer

Two dimensional figures are also called plane figures.

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True

Q82Short answer

A cone is a polyhedron. 15-04-2018

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False

Q83Short answer

A prism has four bases.

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False

Q84Short answer

The number of lines of symmetry of a regular polygon is equal to the vertices of the polygon.

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True

Q85Short answer

The order of rotational symmetry of a figure is 4 and the angle of rotation is 180° only.

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False

Q86Short answer

After rotating a figure by 120° about its centre, the figure coincides with its original position. This will happen again if the figure is rotated at an angle of 240°.

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True

Q87Short answer

Mirror reflection leads to symmetry always.

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False

Q88Short answer

Rotation turns an object about a fixed point which is known as centre of rotation.

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True

Q89Short answer

Isometric sheet divides the paper into small isosceles triangles made up of dots or lines.

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False

Q90Short answer

The circle, the square, the rectangle and the triangle are examples of plane figures.

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True

Q91Short answer

The solid shapes are of two-dimensional.

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False

Q92Short answer

Triangle with length of sides as 5 cm, 6 cm and 11 cm can be con- structed.

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False

Q93Multiple choice

Draw the top, side and front views of the solids given below in Figures 12.21 and 12.22:

This question refers to a figure in the original PDF.

(i)Fig. 12.21
(ii)Fig. 12.22 15-04-2018 Three-dimensional figures often look different from different points of view. You can use centimetre cubes to help you visualize and sketch three- dimensional figures. 1. Use centimetre cubes to build the three-dimensional figure at right. 2. Now view the figure from the front and draw what you see.Then view the figure from the top and draw what you see. Finally, view the figure from the side and draw what you see. Front Top Side 1. How many cubes did you use to build the three-dimensional figure? 2. How could you add a cube to the figure without changing the top view ? 3. How could you remove a cube from the figure without changing the side view ?

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(i) Fig. 12.21

(ii) Fig. 12.22 15-04-2018 Three-dimensional figures often look different from different points of view. You can use centimetre cubes to help you visualize and sketch three- dimensional figures. 1. Use centimetre cubes to build the three-dimensional figure at right. 2. Now view the figure from the front and draw what you see.Then view the figure from the top and draw what you see. Finally, view the figure from the side and draw what you see. Front Top Side 1. How many cubes did you use to build the three-dimensional figure? 2. How could you add a cube to the figure without changing the top view ? 3. How could you remove a cube from the figure without changing the side view ?

Q94Short answer

Draw a solid using the top. side and front views as shown below. [Use Isometric dot paper].

Q95Short answer

Construct a right-angled triangle whose hypotenuse measures 5 cm and one of the other sides measures 3.2 cm.

Q96Short answer

Construct a right-angled isosceles triangle with one side (other than hypotenuse) of length 4.5 cm. 15-04-2018

Q97Short answer

Draw two parallel lines at a distance of 2.2 cm apart.

Q98Short answer

Draw an isosceles triangle with each of equal sides of length 3 cm and the angle between them as 45°.

Q99Short answer

Draw a triangle whose sides are of lengths 4 cm, 5 cm and 7 cm.

Q100Short answer

Construct an obtuse angled triangle which has a base of 5.5 cm and base angles of 30° and 120°.

Q101Short answer

Construct an equilateral triangle ABC of side 6 cm.

Q102Short answer

By what minimum angle does a regular hexagon rotate so as to coincide with its origional position for the first time?

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60° OSKNRKPNOV ONQL Figure Number of Lines of Symmetry Order of Rotation of Symmetry a 1 1 b 1 1 c 1 1 d 2 2 e 1 2 f 0 1 g 1 1 h 0 3 i 4 4 j 1 1 k 0 1 l 1 1 m 0 2 n 0 1 o 1 1 p 1 1 q 1 1 r 0 3 s 3 3 t 1 1 u 10 10 v 3 3 w 0 1

Q103Short answer

In each of the following figures, write the number of lines of symme- try and order of rotational symmetry. Fig. 12.23 [Hint: Consider these as 2-D figures not as 3-D objects.]

This question refers to a figure in the original PDF.

Q104Multiple choice

In the figure 12.24 of a cube,

(i)Which edge is the intersection of faces EFGH and EFBA?
(ii)Which faces intersect at edge FB? 15-04-2018
(iii)Which three faces form the vertex A?
(iv)Which vertex is formed by the faces ABCD, ADHE and CDHG? (v) Give all the edges that are parallel to edge AB. (vi) Give the edges that are neither parallel nor perpendicular to edge BC. (vii) Give all the edges that are perpendicular to edge AB. (viii) Give four vertices that do not all lie in one plane.

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(i) Which edge is the intersection of faces EFGH and EFBA?

(ii) Which faces intersect at edge FB? 15-04-2018

(iii) Which three faces form the vertex A?

(iv) Which vertex is formed by the faces ABCD, ADHE and CDHG? (v) Give all the edges that are parallel to edge AB. (vi) Give the edges that are neither parallel nor perpendicular to edge BC. (vii) Give all the edges that are perpendicular to edge AB. (viii) Give four vertices that do not all lie in one plane.

Q105Short answer

Draw a net of a cuboid having same breadth and height, but length Fig. 12.24 double the breadth.

This question refers to a figure in the original PDF.

Q106Multiple choice

Draw the nets of the following:

(i)Triangular prism
(ii)Tetrahedron
(iii)Cuboid

Q107Short answer

Draw a net of the solid given in the figure 12.25: Fig. 12.25

This question refers to a figure in the original PDF.

Q108Short answer

Draw an isometric view of a cuboid 6 cm × 4 cm × 2 cm.

Q109Multiple choice

The net given below in Fig. 12.26 can be used to make a cube.

This question refers to a figure in the original PDF.

(i)Which edge meets AN?
(ii)Which edge meets DE? Fig. 12.26 15-04-2018

Q110Short answer

Draw the net of triangular pyramid with base as equilateral triangle of side 3 cm and slant edges 5 cm.

Q111Short answer

Draw the net of a square pyramid with base as square of side 4 cm and slant edges 6 cm.

Q112Long answer

Draw the net of rectangular pyramid with slant edge 6 cm and base as rectangle with length 4 cm and breadth 3 cm. 1. Use centimetre cubes to build a figure that has the front, tops and side views shown. Front Top Side 2. You can build the figure by first making a simple figure that matches the front views. 3. Now add cubes so that the figure matches the top view. 4. Finally, remove cubes so that the figure matches the side view. Check that the front and top views are still correct for the figure that you built. Discuss whether there is another step-by-step method for building the above figure. If so, is the final result the same. 15-04-2018

Q113Multiple choice

Find the number of cubes in each of the following figures and in each case give the top, front, left side and right side view (arrow indicating the front view).

(a)
(b)
(c)
(d)(e) (f) (g) (h)

Q114Multiple choice

Draw all lines of symmetry for each of the following figures as given below: (a) (b) (c) 1. Use centimetre cubes to build each three-dimensional figure given below. Then sketch the front, top and side views.

(i)
(ii)
(iii)
(iv)15-04-2018

Q115Short answer

How many faces does Fig. 12.27 have? Fig. 12.27

This question refers to a figure in the original PDF.

Q116Multiple choice

Trace each figure. Then draw all lines of symmetry, if it has.

Q117Multiple choice

Tell whether each figure has rotational symmetry or not.

(a)
(b)
(c)
(d)(e) (f)

Q118Multiple choice

Draw all lines of symmetry for each of the following figures.

(a)
(b)15-04-2018
(c)
(d)(e) (f)

Q119Multiple choice

Tell whether each figure has rotational symmetry. Write yes or no.

Q120Short answer

Does the Fig. 12.28 have rotational symmetry ? Fig. 12.28 15-04-2018

This question refers to a figure in the original PDF.

Q121Short answer

The flag of Japan is shown below. How many lines of symmetry does the flag have? Fig. 12.29

This question refers to a figure in the original PDF.

Q122Multiple choice

Which of the figures given below have both line and rotational symmetry?

(a)
(b)
(c)
(d)15-04-2018

Q123Multiple choice

Which of the following figures do not have line symmetry?

Q124Long answer

Which capital letters of English alphabet have no line of symmetry? 1. Crossword Puzzle Solve the crossword and fill the given box across, downward as per the mentioned clue in the boxes. Across Down 1. The sketch of a solid in 2. The fixed point around which the measurements which the object is rotated. are kept proportional. 3. Two or more lines which 4. The solid shape which does remain apart at a constant not have a vertex or edge. distance, even if extended indefinitely. 5. The 3-D figure which has a 6. The line where two faces of Joker’s cap. a 3-D figure meet. 7. A 2-D figure which has 8. The skeleton 2-D figure unlimited lines of symmetry which when folded results and an infinite order of in a 3-D shape. rotation. 9. The solid which has 5 faces- 10. Shadow of a cube. 3 of which are rectangles and 2 are triangles. 15-04-2018 2. Crazy Cubes Make four cubes with paper and tape, numbering each face as shown. The goal is to line up the cubes so that 1, 2, 3 and 4 can be seen along the top, bottom, front and back of the row of cubes. They can be in any order, and the numbers do not have to be right side up. 15-04-2018