Question

Find the area of the shaded portion. A circle is inscribed in a square such that both their centers coincide. BDE is an isosceles triangle. The side of a square is 10 m.
[4 MARKS]

Answer 1

Formula: [1 Mark]
Steps: [1 Mark]
Application: [1 Mark]
Answer: [1 Marks]

Given that
The side of the square= 10 m.
Now the diameter of the circle will be equal to the side of the square= 10 m.

Area of the square =$a^2$
Area of the square is (10) $\times$ (10) = 100 $m^2$

Given diameter of circle = 10 m

Radius of the circle=$\frac{10}{2}$ =5 m

Area of the circle

= $\pi$ $\times$ ($r^2$)
=$\pi$ $\times$ ($5^2$)

= 78.5$m^2$

Area of the triangle

= $12$ $\times$ (BD) $\times$ (DE)

= 0.5 $\times$ (10) $\times$ (10)

= 50 $m^2$

Area of the shaded region

=Area of square - Area of circle + Area of triangle

= 71.5 $m^2$

So, the area of the shaded region is 71.5 $m^2$.