Question

find the area of the shaded region in the given figure, if ABCD is a square of side 14 cm and APD and BPC are semi circles

Answer 1

Answer:

Step-by-step explanation:

Ans =42 cm

Answer 2

Answer:  The answer is 42 cm².

Step-by-step explanation:  We are given to find the area of the shaded region in the figure.

Given that ABCD is a square of side 14 cm, so the area of the square ABCD is given by

$A_s=14\times 14=196~\textup{cm}^2.$

Now, the radius of the semi-circles AD and BC is

$r=\dfrac{14}{2}=7~\textup{cm}.$

Therefore, the total area of the semi-circles AD and BC is given by

$A_{AD, BC}=2\times \dfrac{\pi\times7^2}{2}=49\pi=49\times \dfrac{22}{7}=154~\textup{cm}^2.$

Therefore, the area of the shaded region is

$A_{shaded}=A_s-A_{AD,BC}=196-154=42~\textup{cm}^2.$

Thus, the answer is 42 cm².