Calculate the area of the shaded region :"

Given :

The figure of circle inscribed in a trapezium is given.

To find :

We have to find the area of the shaded region.

Solution :

The outer figure forms a trapezium whose height is twice the radius of the circle.

Therefore,

Area of the trapezium $= \frac{1}{2} \times 21 \times (19+29) cm^2$

                                        $= \frac{1}{2} \times 21 \times 48  cm^2$ 

                                        $= 21\times24 cm^2$

                                       $= 504 cm^2$.

Area of the inner figure(circle) $= π r^2$ 

Diameter of the inner circle $= 21 cm$

Radius of the circle $= \frac{21}{2}$cm

Area of the circle $= \frac{22}{7} \times \frac{21}{2} \times \frac{21}{2}$

                               $=11\times3\times \frac{21}{2}$

                               $=\frac{693}{2} cm^2$

                               $= 346.5 cm^2$.

$Area of the shaded portion = Area of the trapezium - Area of the circle$

                                                  $= 504-346.5 cm^2$

                                                  $= 157.5 cm^2$

Area of the shaded region is $157.5 cm^2$

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Updated on: 10-Oct-2022

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