Chapter 9

The word circumference contains the prefix circum-, which means “around”. What do you think about the circumference of a circle?

The Greek prefix peri- means “around,” and the root meter means “means of measuring.” “What do you suppose perimeter means?

The Greek prefix dia- means “across.” What do you think about the diameter of a circle?

A wire is bent to form a square of side 22 cm. If the wire is rebent to form a circle, its radius is

• (a)22 cm
• (b)14 cm
• (c)11 cm
• (d)7 cm 1. Give the formula for the area of a circle in terms of the diameter d.

Area of the circle obtained in Question 4 is

• (a)196 cm2
• (b)212 cm2
• (c)616 cm2
• (d)644 cm2

Area of a rectangle and the area of a circle are equal. If the dimensions of the rectangle are 14cm × 11 cm, then radius of the circle is

• (a)21 cm
• (b)10.5 cm
• (c)14 cm
• (d)7 cm.

Area of shaded portion in Fig. 9.15 is

This question refers to a figure in the original PDF.

• (a)25 cm2
• (b)15 cm2
• (c)14 cm2
• (d)10 cm2 Fig. 9.15

Area of parallelogram ABCD (Fig. 9.16) is not equal to

This question refers to a figure in the original PDF.

• (a)DE × DC
• (b)BE × AD
• (c)BF × DC
• (d)BE × BC 15-04-2018 Fig. 9.16 1. Describe what happens to the area of a triangle when the base is doubled and the height remains the same. 2. Describe what happens to the area of a parallelogram when the length of its base is doubled but the height remains the same.

Area of triangle MNO of Fig. 9.17 is Fig. 9.17 1 1 1 1

This question refers to a figure in the original PDF.

• (a)MN × NO
• (b)NO × MO
• (c)MN × OQ
• (d)NO ×OQ 2 2 2 2

Ratio of area of ∆MNO to the area of parallelogram MNOP in the same figure 9.17 is

• (a)2 : 3
• (b)1:1
• (c)1:2
• (d)2 : 1

Ratio of areas of ∆ MNO, ∆MOP and ∆MPQ in Fig. 9.18 is

This question refers to a figure in the original PDF.

• (a)2 : 1 : 3
• (b)1:3:2
• (c)2 : 3 : 1
• (d)1 : 2 : 3 15-04-2018 Fig. 9.18

In Fig. 9.19, EFGH is a parallelogram, altitudes FK and FI are 8 cm and 4cm respectively. If EF = 10 cm, then area of EFGH is

This question refers to a figure in the original PDF.

• (a)20 cm2
• (b)32 cm2
• (c)40 cm2
• (d)80 cm2 Fig. 9.19 The Taj Mahal, a world famous structure, is the most visited attraction in India. It was created in the 17th century by Emperor Shah Jahan to honour the memory of his beloved wife Mumtaz Mahal. The design of the Taj Mahal is based on the number four and its multiples. Think about it 1. The garden at the Taj Mahal was laid out in four squares of the same size. Each square was divided into four flower beds, with 400 flowers in each bed. How many flowers were in the garden? 2. The central chamber of the Taj Mahal was built in the shape of an octagon. How is an octagon related to the number 4? 15-04-2018

In reference to a circle the value of is equal to area area

• (a)
• (b)circumference diameter circumference circumference
• (c)
• (d)diameter radius

Circumference of a circle is always

• (a)more than three times of its diameter
• (b)three times of its diameter
• (c)less than three times of its diameter
• (d)three times of its radius

Area of triangle PQR is 100 cm2 (Fig. 9.20). If altitude QT is 10 cm, then its base PR is

This question refers to a figure in the original PDF.

• (a)20 cm
• (b)15 cm
• (c)10 cm
• (d)5 cm Fig. 9. 20

In Fig. 9.21, if PR = 12 cm, QR = 6 cm and PL = 8 cm, then QM is Fig. 9.21

This question refers to a figure in the original PDF.

• (a)6 cm
• (b)9 cm
• (c)4 cm
• (d)2 cm 15-04-2018

In Fig. 9.22 ∆ MNO is a right-angled triangle. Its legs are 6 cm and 8 cm long. Length of perpendicular NP on the side MO is Fig. 9.22

This question refers to a figure in the original PDF.

• (a)4.8 cm
• (b)3.6 cm
• (c)2.4 cm
• (d)1.2 cm

Area of a right-angled triangle is 30 cm2. If its smallest side is 5 cm, then its hypotenuse is

• (a)14 cm
• (b)13 cm
• (c)12 cm
• (d)11cm

Circumference of a circle of diameter 5 cm is

• (a)3.14 cm
• (b)31.4 cm
• (c)15.7 cm
• (d)1.57 cm

Circumference of a circle disc is 88 cm. Its radius is

• (a)8 cm
• (b)11 cm
• (c)14 cm
• (d)44 cm a. The Taj Mahal stands on a square platform that is 95.40 m on each side. What is the area of this square in square metres? b. The floor area of the main building is 3214 m2. What is the area of the part of the platform that is not covered by the main building? 15-04-2018

Length of tape required to cover the edges of a semicircular disc of radius 10 cm is

• (a)62.8 cm
• (b)51.4 cm
• (c)31.4 cm
• (d)15.7 cm

Area of circular garden with diameter 8 m is

• (a)12.56 m2
• (b)25.12 m2
• (c)50.24 m2
• (d)200.96 m2

Area of a circle with diameter ‘m’ radius ‘n’ and circumference ‘p’ is

• (a)2 n
• (b)m2
• (c)p2
• (d)n2

A table top is semicircular in shape with diameter 2.8 m. Area of this table top is

• (a)3.08 m2
• (b)6.16 m2
• (c)12.32 m2
• (d)24.64 m2

If 1m2 = x mm2 , then the value of x is

• (a)1000
• (b)10000
• (c)100000
• (d)1000000

If p squares of each side 1mm makes a square of side 1cm, then p is equal to

• (a)10
• (b)100
• (c)1000
• (d)10000

12 m2 is the area of

• (a)a square with side 12 m
• (b)12 squares with side 1m each
• (c)3 squares with side 4 m each
• (d)4 squares with side 3 m each

If each side of a rhombus is doubled, how much will its area increase?

• (a)1.5 times
• (b)2 times
• (c)3 times
• (d)4 times

If the sides of a parallelogram are increased to twice its original lengths, how much will the perimeter of the new parallelogram?

• (a)1.5 times
• (b)2 times
• (c)3 times
• (d)4 times

If radius of a circle is increased to twice its original length, how much will the area of the circle increase?

• (a)1.4 times
• (b)2 times
• (c)3 times
• (d)4 times

What will be the area of the largest square that can be cut out of a circle of radius 10 cm?

• (a)100 cm2
• (b)200 cm2
• (c)300 cm2
• (d)400 cm2 15-04-2018 Thirty-seven specialists including artists, stone cutters, engineers, architects, calligraphers, and inlayers designed the Taj Mahal and supervised the 20,000 workers who built it. This section of flooring from a terrace at the Taj Mahal is inlaid with white marble and red sandstone tiles. What geometric shapes do you see in the pattern in the floor? The design and construction of the terrace must have involved measuring lengths and finding areas.

What is the radius of the largest circle that can be cut out of the rectangle measuring 10 cm in length and 8 cm in breadth?

• (a)4 cm
• (b)5 cm
• (c)8 cm
• (d)10 cm

The perimeter of the figure ABCDEFGHIJ is

This question refers to a figure in the original PDF.

• (a)60 cm
• (b)30 cm
• (c)40 cm
• (d)50 cm Fig. 9.23

The circumference of a circle whose area is 81πr2, is

• (a)9πr
• (b)18πr
• (c)3πr
• (d)81πr

The area of a square is 100 cm2. The circumference (in cm) of the largest circle cut of it is

• (a)5 π
• (b)10 π
• (c)15 π
• (d)20 π 15-04-2018

If the radius of a circle is tripled, the area becomes

• (a)9 times
• (b)3 times
• (c)6 times
• (d)30 times

The area of a semicircle of radius 4r is

• (a)8πr2
• (b)4πr2
• (c)12πr2
• (d)2πr2 In Questions 38 to 56, fill in the blanks to make the statements true.

Perimeter of a regular polygon = length of one side × ___________.

If a wire in the shape of a square is rebent into a rectangle, then the of both shapes remain same, but may varry.

Area of the square MNOP of Fig. 9.24 is 144 cm2. Area of each triangle is .

This question refers to a figure in the original PDF.

In Fig. 9.25, area of parallelogram BCEF is cm2 where ACDF is Fig. 9.24 a rectangle. Fig. 9.25

This question refers to a figure in the original PDF.

To find area, any side of a parallelogram can be chosen as of the parallelogram.

Perpendicular dropped on the base of a parallelogram from the opposite vertex is known as the corresponding of the base.

The distance around a circle is its . 15-04-2018

Ratio of the circumference of a circle to its diameter is denoted by symbol .

If area of a triangular piece of cardboard is 90 cm 2, then the length of altitude corresponding to 20 cm long base is cm.

Value of is approximately.

Circumference ‘C’ of a circle can be found by multiplying diameter ‘d’ with .

Circumference ‘C’ of a circle is equal to 2 × .

1 m2 = cm2.

1 cm2 = mm2.

1 hectare = m2.

Area of a triangle = base × .

1 km = m2.

Area of a square of side 6 m is equal to the area of squares of each side 1 cm.

10 cm2 = m2. In Questions 57 to 72, state whether the statements are True or False.

In Fig. 9.26, perimeter of (ii) is greater than that of (i), but its area is smaller than that of (i). (i) (ii) Fig. 9.26 Some of the designs created on the walls of the Taj Mahal can be made using rectangles and triangles. You can use what you know about the area of parallelograms to find the area of triangles. 15-04-2018

This question refers to a figure in the original PDF.

In Fig. 9.27,

This question refers to a figure in the original PDF.

• (a)area of (i) is the same as the area of (ii). (i) (ii) Fig. 9.27
• (b)Perimeter of (ii) is the same as (i).
• (c)If (ii) is divided into squares of unit length, then its area is 13 unit squares.
• (d)Perimeter of (ii) is 18 units.

If perimeter of two parallelograms are equal, then their areas are also equal.

All congruent triangles are equal in area.

All parallelograms having equal areas have same perimeters. Observe all the four triangles FAB, EAB, DAB and CAB as shown in Fig. 9.28: Fig. 9.28 15-04-2018 Now answer Questions 62 to 65:

This question refers to a figure in the original PDF.

All triangles have the same base and the same altitude.

All triangles are congruent.

All triangles are equal in area.

All triangles may not have the same perimeter.

In Fig. 9.29 ratio of the area of triangle ABC to the area of triangle ACD is the same as the ratio of base BC of triangle ABC to the base CD of triangle ACD. Fig. 9.29

This question refers to a figure in the original PDF.

Triangles having the same base have equal area.

Ratio of circumference of a circle to its radius is always 2π : I.

5 hectare = 500 m2

An increase in perimeter of a figure always increases the area of the figure.

Two figures can have the same area but different perimeters.

Out of two figures if one has larger area, then its perimeter need not to be larger than the other figure.

A hedge boundary needs to be planted around a rectangular lawn of size 72 m × 18 m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all? 15-04-2018

People of Khejadli village take good care of plants, trees and animals. They say that plants and animals can survive without us, but we can not survive without them. Inspired by her elders Amrita marked some land for her pets (camel and ox ) and plants. Find the ratio of the areas kept for animals and plants to the living area. Fig. 9.30

This question refers to a figure in the original PDF.

The perimeter of a rectangle is 40 m. Its length is four metres less than five times its breadth. Find the area of the rectangle.

A wall of a room is of dimensions 5 m × 4 m. It has a window of dimensions 1.5 m × 1m and a door of dimensions 2.25 m × 1m. Find the area of the wall which is to be painted.

Rectangle MNOP is made up of four congruent rectangles (Fig. 9.31). If the area of one of the rectangles is 8 m2 and breadth is 2 m, then find the perimeter of MNOP. Square units are also used to measure area in the metric system. Since each small square is 1 cm by 1 cm, it has an area of 1 square centimetre (1 cm2). 15-04-2018 Fig. 9.31

This question refers to a figure in the original PDF.

In Fig. 9.32, area of ∆ AFB is equal to the area of parallelogram ABCD. If altitude EF is 16 cm long, find the altitude of the parallelogram to the base AB of length 10 cm. What is the area of ∆DAO, where O is the mid point of DC? Fig. 9.32 Did You Know Area is expressed in square units, such as square metre or square centimetres. You can abbreviate square units by writing the abbreviation for the unit followed by a power raised 2. For example, an abbreviation for squares metre is m2. Volume is expressed in cubic units. You can abbreviate cubic units by writing the abbreviation for the unit followed by a power raised 3. For example, an abbreviation for cubic centimetres is cm3. 15-04-2018

This question refers to a figure in the original PDF.

Ratio of the area of ∆ WXY to the area of ∆ WZY is 3 : 4 (Fig. 9.33). If the area of ∆ WXZ is 56 cm2 and WY = 8 cm, find the lengths of XY and YZ. Fig. 9.33

This question refers to a figure in the original PDF.

Rani bought a new field that is next to one she already owns (Fig. 9.34). This field is in the shape of a square of side 70 m. She makes a semi circular lawn of maximum area in this field.

This question refers to a figure in the original PDF.

• (i)Find the perimeter of the lawn.
• (ii)Find the area of the square field excluding the lawn. Fig. 9.34

In Fig. 9.35, find the area of parallelogram ABCD if the area of shaded triangle is 9 cm2. Fig. 9.35 15-04-2018

This question refers to a figure in the original PDF.

Pizza factory has come out with two kinds of pizzas. A square pizza of side 45 cm costs 150 and a circular pizza of diameter 50 cm costs 160 (Fig. 9.36). Which pizza is a better deal? Fig. 9.36

This question refers to a figure in the original PDF.

Three squares are attached to each other as shown in Fig. 9.37. Each square is attached at the mid point of the side of the square to its right. Find the perimeter of the complete figure. Fig. 9.37 Visual displays can help you relate ideas and organise information. Copy and extend the concept map to connect ideas you have learned about area. Add on units of measure, formulas, and notes about relationships. 15-04-2018

This question refers to a figure in the original PDF.

In Fig. 9.38, ABCD is a square with AB = 15 cm. Find the area of the square BDFE. Fig. 9.38

This question refers to a figure in the original PDF.

In the given triangles of Fig. 9.39, perimeter of ∆ABC = perimeter of ∆PQR. Find the area of ∆ABC. Fig. 9.39

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Altitudes MN and MO of parallelogram MGHK are 8 cm and 4 cm long respectively (Fig. 9.40). One side GH is 6 cm long. Find the perimeter of MGHK. Fig. 9.40 15-04-2018

This question refers to a figure in the original PDF.

In Fig. 9.41, area of ∆PQR is 20 cm2 and area of ∆PQS is 44 cm2. Find the length RS, if PQ is perpendicular to QS and QR is 5cm. Fig. 9.41

This question refers to a figure in the original PDF.

Area of an isosceles triangle is 48 cm2. If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.

Perimeter of a parallelogram shaped land is 96 m and its area is 270 square metres. If one of the sides of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m (Fig. 9.42). Fig. 9.42 Circles What is the maximum number of times that six circles of the same size can intersect? To find the answer, start by drawing two circles that are of the same size. What is the greatest number of times they can intersect? Add another circle, and another, and so on. 15-04-2018

This question refers to a figure in the original PDF.

Area of a triangle PQR right-angled at Q is 60 cm2 (Fig. 9.43). If the smallest side is 8cm long, find the length of the other two sides. Fig. 9.43

This question refers to a figure in the original PDF.

In Fig. 9.44 a rectangle with perimeter 264 cm is divided into five congruent rectangles. Find the perimeter of one of the rectangles. Fig. 9.44

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Find the area of a square inscribed in a circle whose radius is 7 cm (Fig. 9.45). [Hint: Four right-angled triangles joined at right angles to form a square] Fig. 9.45

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Find the area of the shaded portion in question 92. 15-04-2018 In Questions 94 to 97 find the area enclosed by each of the following figures : 94. Fig. 9.46 95. Fig. 9.47 96. Fig. 9.48 97. Fig. 9.49 15-04-2018 In Questions 98 and 99 find the areas of the shaded region: 98. Fig. 9.50 99. Fig. 9.51 100. A circle with radius 16 cm is cut into four equal parts and rearranged to form another shape as shown in Fig. 9.52: Fig. 9.52 15-04-2018 Does the perimeter change? If it does change, by how much does it increase or decrease? 101. A large square is made by arranging a small square surrounded by four congruent rectangles as shown in Fig. 9.53. If the perimeter of each of the rectangle is 16 cm, find the area of the large square. Fig. 9.53 The figures show how a fractal called the Koch snowflake is formed. It is constructed by first drawing an equilateral triangle. Then triangles with sides one-third the length of the original sides are added to the middle of each side. The second step is then repeated over and over again. The area and perimeter of each figure is larger than that of the one before it. However, the area of any figure is never greater than the area of the shaded box, while the perimeters increase without bound. 102. ABCD is a parallelogram in which AE is perpendicular to CD (Fig. 9.54). Also AC = 5 cm, DE = 4 cm, and the area of ∆ AED = 6 cm2. Find the perimeter and area of ABCD. 15-04-2018 Fig. 9.54 103. Ishika has designed a small oval race track for her remote control car. Her design is shown in the figure 9.55. What is the total distance around the track? Round your answer to the nearest whole cm. Fig. 9.55 Shape up Rectangles The square below has been divided into four rectangles. The areas of two of the rectangles are given. If the length of each of the segments in the diagram is an integer, what is the area of the original square? (Hint: Remember a + c = b + d) Use different lengths and a different answer to create your own version of this puzzle. 15-04-2018 104. A table cover of dimensions 3 m 25 cm × 2 m 30 cm is spread on a table. If 30 cm of the table cover is hanging all around the table, find the area of the table cover which is hanging outside the top of the table. Also find the cost of polishing the table top at 16 per square metre. 105. The dimensions of a plot are 200 m × 150 m. A builder builds 3 roads which are 3 m wide along the length on either side and one in the middle. On either side of the middle road he builds houses to sell. How much area did he get for building the houses? 106. A room is 4.5 m long and 4 m wide. The floor of the room is to be covered with tiles of size 15 cm by 10 cm. Find the cost of covering the floor with tiles at the rate of 4.50 per tile. 107. Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1m of fencing costs 300. 108. Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle? 109. How much distance, in metres, a wheel of 25 cm radius will cover if it rotates 350 times? Revise • Does your solution answer the question? When you think you have solved a problem, think again. Your answer may not really be the solution to the problem. For example, you may solve an equation to find the value or a variable, but to find the answer the problem is asking for, the value of the variable may need to be substituted into an expression. 15-04-2018 110. A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path. 111. A carpet of size 5 m × 2 m has 25 cm wide red border. The inner part of the carpet is blue in colour (Fig. 9.56). Find the area of blue portion. What is the ratio of areas of red portion to blue portion? Fig. 9.56 112. Use the Fig. 9.57 showing the layout of a farm house: Fig. 9.57

This question refers to a figure in the original PDF.

• (a)What is the area of land used to grow hay?
• (b)It costs 91 per m2 to fertilise the vegetable garden. What is the total cost?
• (c)A fence is to be enclosed around the house. The dimensions of the house are 18.7 m ×12.6 m. At least how many metres of fencing are needed?
• (d)Each banana tree required 1.25 m2 of ground space. How many banana trees can there be in the orchard? 15-04-2018 113. Study the layout given below in Fig. 9.58 and answer the questions: Fig. 9.58 (a) Write an expression for the total area covered by both the bedrooms and the kitchen. (b) Write an expression to calculate the perimeter of the living room. (c) If the cost of carpeting is 50/m2, write an expression for calculating the total cost of carpeting both the bedrooms and the living room. (d) If the cost of tiling is 30/m2, write an expression for calculating the total cost of floor tiles used for the bathroom and kitchen floors. (e) If the floor area of each bedroom is 35 m2, then find x. 114. A 10 m long and 4 m wide rectangular lawn is in front of a house. Along its three sides a 50 cm wide flower bed is there as shown in Fig. 9.58. Find the area of the remaining portion. Fig. 9.59 15-04-2018 115. A school playground is divided by a 2 m wide path which is parallel to the width of the playground, and a 3 m wide path which is parallel to the length of the ground (Fig. 9.60). If the length and width of the playground are 120 m and 80 m respectively, find the area of the remaining playground. Fig. 9.60 116. In a park of dimensions 20 m × 15 m, there is a L shaped 1m wide flower bed as shown in Fig. 9.61. Find the total cost of manuring for the flower bed at the rate of Rs 45 per m 2. Fig. 9.61 117. Dimensions of a painting are 60 cm × 38 cm. Find the area of the wooden frame of width 6 cm around the painting as shown in Fig. 9.62. Fig. 9.62 15-04-2018 118. A design is made up of four congruent right triangles as shown in Fig. 9.63. Find the area of the shaded portion. Fig. 9.63 119. A square tile of length 20 cm has four quarter circles at each corner as shown in Fig. 9.64(i). Find the area of shaded portion. Another tile with same dimensions has a circle in the centre of the tile [Fig. 9.64 (ii)]. If the circle touches all the four sides of the square tile, find the area of the shaded portion. In which tile, area of shaded portion will be more? (Take = 3.14) (i) (ii) Fig. 9.64 120. A rectangular field is 48 m long and 12 m wide. How many right triangular flower beds can be laid in this field, if sides including the right angle measure 2 m and 4 m, respectively? 15-04-2018 121. Ramesh grew wheat in a rectangular field that measured 32 metres long and 26 metres wide. This year he increased the area for wheat by increasing the length but not the width. He increased the area of the wheat field by 650 square metres. What is the length of the expanded wheat field? 122. In Fig. 9.65, triangle AEC is right-angled at E, B is a point on EC, BD is the altitude of triangle ABC, AC = 25 cm, BC = 7 cm and AE = 15 cm. Find the area of triangle ABC and the length of DB. Fig. 9.65 123. 15-04-2018 124. Calculate the area of shaded region in Fig. 9.66, where all of the short line segments are at right angles to each other and 1 cm long. Fig. 9.66 125. The plan and measurement for a house are given in Fig. 9.67. The house is surrounded by a path 1m wide. Fig. 9.67 Find the following: (i) Cost of paving the path with bricks at rate of 120 per m2. (ii) Cost of wooden flooring inside the house except the bathroom at the cost of 1200 per m2. (iii) Area of Living Room. 15-04-2018 126. Architects design many types of buildings. They draw plans for houses, such as the plan shown in Fig. 9.68: Fig. 9.68 An architect wants to install a decorative moulding around the ceilings in all the rooms. The decorative moulding costs 500/metre. (a) Find how much moulding will be needed for each room. (i) family room (ii) living room (iii) dining room (iv) bedroom 1 (v) bedroom 2 (b) The carpet costs 200/m2. Find the cost of carpeting each room. (c) What is the total cost of moulding for all the five rooms. 127. ABCD is a given rectangle with length as 80 cm and breadth as 60 cm. P, Q, R, S are the mid points of sides AB, BC, CD, DA respectively. A circular rangoli of radius 10 cm is drawn at the centre as shown in Fig. 9.69. Find the area of shaded portion. 15-04-2018 Fig. 9.69 128. 4 squares each of side 10 cm have been cut from each corner of a rectangular sheet of paper of size 100 cm × 80 cm. From the remaining piece of paper, an isosceles right triangle is removed whose equal sides are each of 10 cm length. Find the area of the remaining part of the paper. 129. A dinner plate is in the form of a circle. A circular region encloses a beautiful design as shown in Fig. 9.70. The inner circumference is 352 mm and outer is 396 mm. Find the width of circular design. Fig. 9.70 130. The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution. (Take π = 3.14) 15-04-2018 131. A photograph of Billiard/Snooker table has dimensions as th of its actual size as shown in Fig. 9.71: Fig. 9.71 The portion excluding six holes each of diameter 0.5 cm needs to be polished at rate of 200 per m2. Find the cost of polishing. For (1) –(4): For the dimensions of the field / court refer the diagram given at the end of the unit. 1. Find the dimensions of a Basket Ball court. (i) Calculate the perimeter of the court. (ii) Calculate the total area of the court. (iii) Find the total area of the bigger central circle of the court. (iv) Find the area of the smaller central circle. (v) Find the difference of areas found in part (iii) and (iv). 2. Find the dimensions of a Badminton court. (i) Calculate the perimeter of the court. (ii) Calculate the total area of the court. (iii) Find the total area of any one side boundaries of the court. (iv) Find the area of a left service court. 15-04-2018 3. In a foot ball field, calculate the (i) total area of the 2 goal posts. (ii) total area covered by the field. (iii) the perimeter of the field. 4. In a hockey field, calculate the (i) area included inside the shooting circles. (ii) the perimeter of Hockey ground. 5. Complete the following data by using the formula for circumference of a circle. Circumference of a circle = 2πr r = radius of the circle Radius Diameter Circumference Foot ball 71 cm Basket ball 24.8 cm Cricket ball 23 cm Volley ball 10.3 cm Hockey ball 22.4 cm Lawn Tennis ball 6.35 cm Shot put 65 mm (Circumference of a ball is used in the sense of circumference of the circle with the same radius). 6. Observe the two rectangles given in Fig. 9.72: Rectangle A has greater area but its perimeter is less than rectangle B. (A) (B) Fig. 9.72 15-04-2018 Now draw the following pair of rectangles: (i) having same area but different perimeter. (ii) having same perimeter but different areas. (iii) One has larger area but smaller perimeter than other. (iv) Area of one rectangle is three times the area of other rectangle but both have the same perimeters. 7. Puzzle In this puzzle, called a “Squared square,” squares of different sizes are contained within one big rectangle. The goal is to find out the sizes of the squares with the questions marks. By comparing known length of lines make some deductions to find out the sizes that are missing. Each number stands for the length of the side in that square. Fig. 9.73 15-04-2018 8. Cross-word Puzzle Solve the given crossword and then fill up the given boxes. Clues are given below for across as well as downward filling. Also for across and down clues, clue number is written at the corner of boxes. Answers of clues have to fill in their respective boxes. 1. 2πr = _______ of a circle of radius r.s. 2. 2 (l + b) = ________ of a rectangle. 3. πr2 = _________ of a circle of radius r. 4. base × height = Area of a _______. 5. side × side = Area of a _______. 6. Area of ________ = × base × altitude. 7. 10000m2 = _______ hectare. 8. ________ = 2 × radius. 15-04-2018 For Activity Q.1. Basket Ball Court For Activity Q.2. Badminton Court 15-04-2018 For Activity Q.3. Foot ball Field For Activity Q.4. Hockey Ground 15-04-2018