Q127 of 131 Page 226

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.

Given, P is the mid point of AB, so AP = 40 cm


And S is the mid point of AD, so AS = 30 cm


Area of ABCD = 80 × 60 = 4,800 cm2


Area of ∆SAP = × AP × AS = × 40 × 30 = 600 cm2


Area of 4 unshaded congruent triangles =4 × 600 cm2 = 2,400 cm2


Area of unshaded circle = ∏r2 = 3.14 × 10 × 10 = 314 cm2


∴ Area of shaded area = 4,800 – (2,400 + 314) = 2086 cm2


More from this chapter

All 131 →
125

The plan and measurement for a house are given in Fig. 9.67. The house is surrounded by a path 1m wide.


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.

 126

Architects design many types of buildings. They draw plans for houses, such as the plan shown in 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.

 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.