Question

In figure ABCD is a square of side 14cm. Semi circles are drawn with each side of square as diameter. Find the area of shaded region

Answer 1

Answer:

area of square -area of 2 semi circles

Answer 2

Recall:

$\text {Area of a square} = \text {Length} \times \text {Length}$

$\text {Area of a triangle} = \dfrac{1}{2} \times \text {Base} \times \text {Height}$

$\text {Area of a circle} = \pi r&2$

* See attached diagram for a more detailed visual representation of the question.

Find the area of the square:

$\text {Area} = \text {Length} \times \text {Length}$

$\text {Area} = 14 \times 14$

$\text {Area} = 196 \text { cm}^2$

Find the area of a quadrant (Region AFOE):

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

$\text{Area} = \dfrac{1}{4} \pi (14 \div 2)^2$

$\text{Area} = 38.5 \text{ cm}^2$

Find the area of the triangle (Region AOE):

$\text {Area} = \dfrac{1}{2} \times \text {Base} \times \text {Height}$

$\text {Area} = \dfrac{1}{2} \times \text {7} \times \text {7}$

$\text {Area} = 24.5 \text { cm}^2$

Find the area of a segment (Region AFO):

$\text {Area} = 38.5 - 24.5$

$\text {Area} = 14 \text { cm}^2$

Find the area of the shaded pink region:

$\text {Area of the shaded region } = \text {Area of the big square } - \text {8 of the segments }$

$\text {Area} =196 - (8 \times 14 )$

$\text {Area} =84 \text { cm}^2$

Answer: The area is 84 cm²