Question

Find the area of the shaded region of the square of side 14cm

Answer 1

hope its help you dear

Answer 2

Answer:

The area of shaded region is 103.54 centimeter square.

Step-by-step explanation:

Given : The square of side 14 cm. The radius of semicircle is 3 cm.

To find : The area of shaded region of the square in the attached figure?

Solution :

The area of a big square with side a=14 cm

$A_b=a^2$

$A_b=14^2$

$A_b=196 cm^2$

The area of 4 semi circle around a smaller square inside a big square with radius r=3 cm,

$A_c=4\times \frac{1}{2}\pi r^2$

$A_c=4\times \frac{1}{2}\times 3.14\times 3^2$

$A_c=2\times 3.14\times 9$

$A_c=56.52 cm^2$

The area of small square with side s=6 cm (twice of 3)

$A_s=s^2$

$A_s=6^2$

$A_s=36 cm^2$

Shaded region = Area of big square -(area of 4 semicircle + area of small square)

$A=A_b-(A_c+A_s)$

$A=196-(56.52+36)$

$A=196-92.52$

$A=103.48cm^2$

Therefore, The area of shaded region is 103.54 centimeter square.