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Question

In Fig. ABCD is a trapezium with ABDC, AB = 18 cm, DC = 32 cm and the distance between AB and DC is 14 cm. Circles of equal radii 7 cm with centres A, B, C and D have been drawn. Then, find the area of the shaded region of the figure. (Use π=227)

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Solution

Given: In trapezium ABCD

AB ║ CD

AB = 18 cm, DC = 32 cm

and distance between AB and DC = 14 cm

Area of trapezium ABCD=12(32+18)14=50×7=350cm2

Now circles are drawn of radii 7 cm from A, B, C, D.

We know that sum of all angles of a trapezium = 360°

⇒area circle inside trapezium with centre ABCD = area of circle with 7 cm = π×72=227×49=154cm2

Hence remaining area = 350 cm2 – 154 cm2

= 196 cm2


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