The area of the shaded region is 5.13 yd square.
A semicircle is given with a radius of 3 yd.
A triangle is placed inside the semicircle.
We need to find the shaded region as shown in the figure.
The shaded region is calculated by subtracting the area of the triangle from the area of the semicircle.
We will use [tex]\pi[/tex] = 3.14.
What is the area of a semicircle and the area of a triangle?
The area of a semicircle is half the area of a circle so we have,
Area of a semicircle = [tex]\frac{1}{2}\pi r^2[/tex]
The area of a triangle is given by:
= 1/2 x base x height
Calculate the area of the semicircle.
Consider r = radius of the semicircle.
The radius of the semicircle = 3 yd
[tex]A = \frac{1}{2}\pi r^2\\\frac{1}{2}\times3.14\times3^2\\\frac{1}{2}\times3.14\times9\\[/tex]
A = 28.26 / 2
A = 14.13 yd square.
Calculate the area of the triangle.
A = 1/2 x base x height
From the given figure we see that,
The base = 2 x radius of the semicircle.
And height = radius of the semicircle.
A = 1/2 x 2r x r
A = 1/2 x 2 x 3 x 3
A = 9 yd square
Now,
Area of shaded region = Area of the semicircle - Area of the triangle
= 14.13 - 9
= 5.13 yd square.
Thus, the area of the shaded region is 5.13 yd square.
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