Question

A triangle is placed in a semicircle with a radius of 6 yd, as shown below. Find the area of the shaded region.

Answer 1

Answer: The area of the shaded region is 20.52 yd^2

Step-by-step explanation: The given figure shows a triangle inserted into a semi circle. The base of the triangle runs from one end of the semi circle to the other, which means the base of the triangle measures the same as the diameter. If the radius of the circle is 6, then the diameter equals 12 yds, (that is radius times 2).

The area of the triangle is given as;

1/2 b x h (that is)

1/2 base x height

Where the base is 12 and the height is 6. The area equals

Area = 1/2 (12) x 6

Area = 6 x 6

Area = 36 yd^2

Also to compute the area of the semi circle, we shall calculate the area of a circle and divide by 2.

Area of a circle is;

Area = pi x R^2

Area = 3.14 x 6^2

Area = 3.14 x 36

Area = 113.04

Area of semi circle = 113.04/2

Area of semi circle = 56.52 yd^2

At this point, subtracting the area of the triangle from the area of the semi circle leaves us with the area of the shaded region. Hence

Area of shaded region = 56.52 - 36

Area of shaded region = 20.52 yd^2