Question

The figure in the diagram is composed of a semi-circle and an equilateral triangle. Find the total area of the figure.

Answer 1

Answer:

D) 82.57

Step-by-step explanation:

Area of the semicircle:

The area of a semicircle is given by:

$A=\frac{\pi r^2}{2}$

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

$A=\frac{\pi\ast5^2}{2}=\frac{25\pi}{2}=12.5\pi=39.27$

Area of the equilateral triangle:

The area of an equilateral triangle with side s is given by:

$A=\frac{\sqrt{3}}{4}s^2$

In this question, s = 10. So

$A=\frac{\sqrt{3}}{4}\ast10^2=\frac{100\sqrt{3}}{4}=25\sqrt{3}=43.30$

Total area:

Sum of the semicircle with the equilateral triangle.

A = 39.27 + 43.30 = 82.57

The correct answer is:

D) 82.57