In the figure given below, find the area of the shaded region, where ABCD is a square of side 14cm in which four semi-circles of same radii are drawn as shown. (Take π=3.14)

Given,
ABCD is a square of side 14 cm in which four semicircles of same radii are drawn.

We know that area of square is given by

A s = (s i d e) 2

.
We get,

A s = (14) 2 ⇒ A s = 196 cm 2

According to the figure,

3 + r + 2 r + r + 3 = 14 ⇒ 4 r + 6 = 14 ⇒ 4 r = 8 ⇒ r = 2 cm

We know that area of a semicircle is

A s c = π r 2 2

.
We get,

A s c = π r 2 2 ⇒ 12 3.14 × 22 ⇒ 6 .28cm 2

Now,
Area of the inner square is given by

A i s = (side) 2

.
We get,

A i s = (side) 2 ⇒ A i s = (4) 2 A i s = 16 cm 2

The area of the shaded region = Area of square – (Area of inner square – Area of 4 semi-circles)
We get,

Area of shaded region = 196 − 16 + 4 × 6.28 ⇒ Area of shaded region = 154.88 cm 2

Therefore, the area of the shaded region is

154.88 cm 2

.
Hence, the correct option is 2.

In the figure given below, find the area of the shaded region, where ABCD is a square of side 14cm in which four semi-circles of same radii are drawn as shown. (Take $π = 3.14)$