Question

$\huge\sf{Question}$
In the adjoining figure, A6CD is a square of side 21 cm. AC and BD are two diagonals of the square. Two semicircle are drawn with AD and BC as diameters. Find the area of the shaded region. 

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Answer 1

Answer:

The area of shaded region is 576cm².

Answer 2

Answer:

Hello!

$\huge\sf{Question}$

In the adjoining figure, A6CD is a square of side 21 cm. AC and BD are two diagonals of the square. Two semicircle are drawn with AD and BC as diameters. Find the area of the shaded region. 

$\huge\bold\red{Answer}$

We know that diagonals of a square are equal and bisect each other at right angles.

AB=BC=CD=DA=21cm

OA=OB=OC=OD.

and

we obtain 4 congruent triangles i.e. AOB,BOC,COD and DOA of equal areas.

Hence,shaded area inside the the square

$= \frac{1}{2}( \sf{area \: of \: square})$

$\frac{1}{2} \times 21 \times 21 \\ \\ = {220.5cm}^{2}$

Shaded area outside and the area ABCD= Area of two semicircles with AD and BC as diameters.

Radius

$= \frac{ad}{2} \\ \\ = \frac{21}{2}$

Area of semicircle

$= \frac{ {\pi r}^{2} }{2} \\ \\ = \frac{22 \times 21 \times 21}{7 \times 2 \times 2 \times 2} \\ \\ = {173.25cm}^{2}$

Area of two semicircles

$= 2 \times 173.25 = {346.5cm}^{2}$

Now area of shaded region

$= 220.5 + 346.5 {cm}^{2} \\ \\ = {567cm}^{2}$

Hope it helps you from my side