Question

in figure a b c and d are the centres of equal circles which touch externally in pairs and ABCD is a square of side 14cm find the area of the shaded region

Answer 1

heya..

Here is your answer...

Answer 2

Given that,

Square of side= 14 cm

According to figure,

Area of each of the 4 sectors is equal to each other and is a sector of 90° in a circle.

We need to calculate the radius of circles with centers

Using formula of radius

$r=\dfrac{side}{2}$

Put the value into the formula

$r=\dfrac{14}{2}$

$r=7\ cm$

So, area of four sectors will be equal to the area of one complete circle

We need to calculate the area of the circle

Using formula of area

$A=\pi r^2$

Put the value into the formula

$A=\pi\times7^2$

$A=154\ cm^2$

We need to calculate the area of the shaded region

Using formula of area

area of the shaded region=area of square ABCD- area of four sectors

Put the value into the formula

$\text{area of the shaded region}=(14)^2-\dfrac{22}{7}\times7^2$

$\text{area of the shaded region}=42\ cm^2$

Hence, The area of the shaded region is 42 cm².