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
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56cm2