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Answer :

(i) Area of the rectangle = l × b

= 18 cm × (6 cm + 4 cm) = 18 cm × 10 cm =\( 180 cm^2\)
Area of right triangle \(\triangle \)AEF

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×6×10=30 cm^2 \)

Area of right \(\triangle BCE = \frac{1}{2} × b × h
= \frac{1}{2} × 8 × 10 =40 cm^2 \)

Area of the two right triangles
=\( 30 cm^2 + 40 cm^2 = 70 cm^2 \)

Area of the shaded portion

= \( 180 cm^2 – 70 cm^2 = 110 cm^2 \)

(ii) Area of the square PQRS =\( (Side)^2
= (20)^2 = 400 cm^2 \)

Area of right triangle \(\triangle \)TSU

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×10×10=50 cm^2 \)

Area of right triangle \(\triangle \)QRU

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)

Area of right triangle \(\triangle \)PQT

=\(\frac{1}{2} ×b×h= \frac{1}{2} ×20×10=100 cm^2 \)

Area of the three triangles

\( = 50 cm^2 + 100 cm^2 + 100 cm^2 = 250 cm^2 \)

Area of the shaded portion

=\( 400 cm^2 – 250 cm^2 = 150 cm^2 \)

- Q.1 A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
- Q.2 . A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.
- Q.3 A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1. 5 cm along each of its sides. Find the total area of the margin.
- Q.4 A verandah of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find: (i) the area of the verandah. (ii) the cost of cementing the floor of the verandah at the rate of Rs. 200 per \( m^2. \)
- Q.5 A path 1 m wide is built along the border and inside a square garden of side 30 m. Find: (i) the area of the path (ii) the cost of planting grass in the remaining portion of the garden at the rate of Rs. 40 per \( m^2.\)
- Q.6 Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.
- Q.7 Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find (i) the area covered by the roads. (ii) the cost of constructing the roads at of the rate of Rs. 110 per\( m^2. \)
- Q.8 Pragya wrapped a card around a circular pipe of radius 4 cm and cut off the length required of the cord. Then she wrapped it around a square box of side 4 cm (also shown). Did she have any cord left? (\(\pi \)= 3.14)
- Q.9 The given figure represents a rectangular lawn with a circular flower bed in the middle. Find: (i) the area of the whole land. (ii) the area of the flower bed. (iii) the area of the lawn excluding the area of the flower bed. (iv) the circumference of the flower bed.
- Q.11 Find the area of the quadrilateral ABCD. Here, AC = 22 cm, BM = 3 cm, DN = 3 cm, and BM \(\perp \)AC, DN \(\perp \)AC.

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