Question

ABCD is a square of side 14cm,a semicircle are drawn inside of square with each side as diameter as shown in the figure.find the area of shaded region

Answer 1

May this will help you

Answer 2

Answer:

The area of the shaded region is $112 cm^{2}$.

Step-by-step explanation:

Let the $4$ shaded regions be I,II,III and IV.

I - shaded region at the top

II - shaded region at the right

III - shaded region at the bottom

IV - shaded region at the left

Area of I $+$ area of III $=$ area of $ABCD$ - area of $2$ semicircles

$= 14 *14 - 2 * \frac{1}{2} *\frac{22}{7} *7*7\\= 196-154\\=42 cm^{2}$( area of semicircle $=\frac{1}{2} *\frac{22}{7} *r^{2}$)

Similarly, area of II $+$ area of IV is $42 cm^{2}$

So, area of the shaded region :

area of $ABCD$ $-$ area of (I$+$II$+$III$+$IV)

$=196-2*42\\=196-84\\=112cm^{2}$

Hence area of the shaded region is $112cm^{2}$.