Find the area of the shaded portion. A circle is inscribed in a square such that both their centres coincide. BDE is an isosceles triangle. The side of a square is 10m.
[4 MARKS]
Formula: 1 Mark
Steps: 1 Mark
Application: 1 Mark
Answer: 1 Marks
Given that,
The side of the square ABCD = 10 m.
Now the diameter of the circle will be equal to the side of the square ABCD = 10 m.
Area of the square = a2
Area of the square is (10) × (10) = 100 m2
Given diameter of circle = 10 m
Radius of the circle = 102 = 5 m
Area of the circle
= π × (r2)
= π × (52)
= 78.5m2
Area of the triangle BDE
= 12 × (BD) × (DE)
= 0.5 × (10) × (10)
= 50 m2
Area of the shaded region
= Area of square ABCD - Area of circle + Area of triangle BDE
= 71.5 m2
So, the area of the shaded region is 71.5 m2.