Question

In Fig. ABCD is a trapezium with $AB\parallel DC$, 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 $\pi =\frac{22}{7}$)

Answer 1

Given: In trapezium ABCD

AB ║ CD

AB = 18 cm, DC = 32 cm

and distance between AB and DC = 14 cm

$AreaoftrapeziumABCD=\frac{1}{2}(32+18)14=50\times 7=350c{m}^2$

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 = $\pi \times 7^2=\frac{22}{7}\times 49=154c{m}^2$

Hence remaining area = 350 $c{m}^2$ – 154 $c{m}^2$

= 196 $c{m}^2$