Question

For the figure find the area of the triangle, area of the circle, and area of the shaded region. Round to the nearest hundredth where necessary.

Answer 1

For this problem, we are given a compound image and we need to calculate the area of the triangle, the shaded region, and the circle.

Let's draw the problem, so we can better understand the problem:

We need to first calculate the area of the large triangle, which is done below:

$A_{triangle}=\frac{40\cdot27}{2}=540\text{ square km}$

Now we need to determine the area of circle, which is given below:

$A_{circle}=\pi(\frac{12}{2})^2=3.14\cdot36=113.04\text{ square km}$

Now we need to determine the shaded area, which is the subtraction between the triangle's area and the circle's. We have:

$A_{shaded}=A_{triangle}-A_{circle}=540-113.04=426.96\text{ square km}$

The area of the triangle is 540 square km, the area of the circle is 113.04 square km and the area of the shaded area is 426.96 square km.