Question

In the given figure, ABCD is a trapezium with AB || 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.
(Use \[\pi = \frac{22}{7}\] 

 

Answer 1

Area of shaded region = Area of trapezium ABCD − Area of 4 sectors

\[= \frac{1}{2}\left( AB + DC \right) \times 14 - \left( \frac{\angle A}{360°}\pi r^2 + \frac{\angle B}{360°}\pi r^2 + \frac{\angle C}{360°}\pi r^2 + \frac{\angle D}{360°}\pi r^2 \right)\]

\[ = \frac{1}{2}\left( AB + DC \right) \times 14 - \left( \frac{\angle A + \angle B + \angle C + \angle D}{360°} \right)\pi r^2 \]

\[ = \frac{1}{2}\left( 18 + 32 \right) \times 14 - \frac{22}{7} \left( 7 \right)^2 \]

\[ = 350 - 154\]

\[ = 196 {cm}^2\]

Hence, the area of shaded region is 196 cm²