Question

In the given figure, ABCD is a square of side 8cm . We need to find the area of shaded region.

Answer 1

Find the Area of segment ABC (See attached):

$\text {Area of the square} = \text{Lengh} \times \text {Length}$

$\text {Area of the square} = 8 \times 8$

$\text {Area of the square} = 64 \text { cm}^2$

$\text {Area of the quadrant} = \dfrac{1}{4} \pi r^2$

$\text {Area of the quadrant} = \dfrac{1}{4} \pi (8)^2$

$\text {Area of the quadrant} = 16\pi \text { cm}^2$

$\text {Area of the segment ABC} = (64 - 16\pi) \text{ cm}^2$

Find 4 of the segments (ABC, BCD, CDA, DAB):

$\text {1 segment } = (64 - 16\pi) \text { cm}^2$

$\text {4 segments } = 4(64 - 16\pi) \text { cm}^2$

Find the area of the shaded part:

$\text {Area of the shaded part} = \text {Area of the square} - \text{Area of the 4 segments}$

$\text {Area of the shaded part} = 64 - 4(64 - 16\pi )$

$\text {Area of the shaded part} = \dfrac{64}{7} \text { cm}^2$

$\text {Area of the shaded part} = 9.14 \text { cm}^2$

Answer: 9.14 cm²