Question

This figure is made up of a triangle and a semicircle.

What is the area of this figure?

Use 3.14 for pi. Round only your final answer to the nearest tenth.

Enter your answer as a decimal

Answer 1

Given is a composite figure where we have a semicircle and a triangle.

To find the area of the semicircle, we need diameter of the circle which is the distance between two given points (2,4) and (2,-3). So the diameter is 4-(-3) = 7 and radius would be 3.5 units.

Area of circle = π·r² = 3.14 × (3.5)² = 38.465 squared units.

So, area of semicircle = 38.465 ÷ 2 = 19.2325 squared units.

To find the area of the triangle, we need base and height of the triangle. The base is same as diameter = 7 and the height would be distance between given point (5,0) and (2,0), so height is 5-2 = 3.

Area of triangle
`=(1)/(2) bh = (1)/(2) (7)(3) = 10.5` 1/2 * 7 * 3 = 10.5 squared units.

Total area = Area of triangle + Area of semicircle = 10.5 + 19.2325 = 29.7325 squared units.

So, final answer is 29.7325 squared units.