Question

28. In figure, find the area of the shaded region, where ABCD is a square of side 14
cm in which four semi-circles of same radii are drawn as shown​

Answer 1

Given :-

• ABCD is a square.

• The side of the square is 14cm

• Four semicircles are given which of same radii

• As it is observed from the figure, that small square is surrounded by 4 semicircles.

Solution :-

Here,

The side of the square is 14 cm

As we know that,

All sides of square are equal .

• Area of large square = Side * Side

Put the values in the required formula,

Area of large square = 14 * 14 = 196cm^2

Now,

It is given that all semicicles have same radii that is 3 cm

Area of 1 semicircle = πr^2/2

Area of 1 semicircle = 22/7 * 3 * /2

Area of 1 semicicle = 33/7 cm

Therefore,

Area of 4 semicircles = 4 * 33/7 = 132/7

= 18.85cm^2

Here,

It is observed from the figure,

The side of small square = Diameter of semicircle

As we know that,

Diameter = 2 R

Diameter = 2 * 3 = 6cm

Now,

Area of small square = Side * Side

Area of small square = 6 * 6 = 36cm^2

The total area of unshaded region

= Area of 4 semicircles + Area of small square.

The total area of unshaded region

= 36 + 18.85 = 54.85

Now,

We have to find the area of shaded region

Therefore,

Area of shaded region = Area of large square - Area of unshaded region

Put the required values,

Area of shaded region = 196 - 54.85

Area of shaded region = 141.15cm^2

Hence, Area of shaded region is 141.15 cm^2$.$