Answer:
The area of the composite figure = 65.1 in.²
Step-by-step explanation:
The given figure is formed from
- A triangle of base 8 inches and height (14 - r) inches where r is the radius of the semi-circle
- A semi-circle of diameter 8 inches
Let us find the areas of the triangle and the semi-circle, then add them up
∵ The diameter of the semi-circle is 8 inches
→ The radius is half the diameter
∴ The radius of the semi-circle = 8 ÷ 2 = 4 inches
→ The area of the semi-circle = [tex]\frac{1}{2}[/tex] πr²
∴ The area of the semi-circle = [tex]\frac{1}{2}[/tex] π(4)²
∴ The area of the semi-circle = [tex]\frac{1}{2}[/tex] π(16)
∴ The area of the semi-circle = 8π in.²
∵ The height of the triangle is (14 - r) in.
∵ r = 4 in.
∴ The height of the triangle = 14 - 4 = 10 in.
→ The area of the triangle = [tex]\frac{1}{2}[/tex] × base × height
∵ The base of the triangle = 8 in.
∴ The area of the triangle = [tex]\frac{1}{2}[/tex] × 8 × 10
∴ The area of the triangle = 40 in.²
→ Add the two areas to find the area of the figure
∵ The area of the composite figure = 8π + 40
∴ The area of the composite figure = 65.13274123 in.²
→ Round it to the nearest tenths place (one decimal place)
∴ The area of the composite figure = 65.1 in.²
