Answer:
D) 82.57
Step-by-step explanation:
Area of the semicircle:
The area of a semicircle is given by:
[tex]A=\frac{\pi r^2}{2}[/tex]
In which r is the radius.
In the semicircle in this question, the diameter is 10. The radius is half the diameter, so r = 10/2 = 5.
Then
[tex]A=\frac{\pi\ast5^2}{2}=\frac{25\pi}{2}=12.5\pi=39.27[/tex]
Area of the equilateral triangle:
The area of an equilateral triangle with side s is given by:
[tex]A=\frac{\sqrt{3}}{4}s^2[/tex]
In this question, s = 10. So
[tex]A=\frac{\sqrt{3}}{4}\ast10^2=\frac{100\sqrt{3}}{4}=25\sqrt{3}=43.30[/tex]
Total area:
Sum of the semicircle with the equilateral triangle.
A = 39.27 + 43.30 = 82.57
The correct answer is:
D) 82.57
