Answer :
Answer:
The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters
Step-by-step explanation:
The area of a triangle = [tex]\frac{1}{2}[/tex] × b × h, where
- b is the length of the base
- h is the length of the height
The area of a semi-circle = [tex]\frac{1}{2}[/tex] π r², where
- r is the length of the radius
∵ The area of the figure = Area Δ - Area semicircle
∵ The area of the figure = [tex]\frac{1}{2}[/tex] × b × h - [tex]\frac{1}{2}[/tex] π r²
∵ The base of the triangle is 12 meters
→ Substitute it in the area of the figure above
∴ The area of the figure = [tex]\frac{1}{2}[/tex] × 12 × h - [tex]\frac{1}{2}[/tex] π r²
∴ The area of the figure = 6h - [tex]\frac{1}{2}[/tex] π r²
∵ The area of the figure = 48 - 2 π
→ Equate the two expressions of the area of the figure
∴ 6h - [tex]\frac{1}{2}[/tex] π r² = 48 - 2 π
→ Equate the like terms of the two sides
∵ 6h = 48
→ Divide both sides by 6 to find h
∴ h = 8
∵ - [tex]\frac{1}{2}[/tex] π r² = -2 π
→ Divide both sides by -π
∴ [tex]\frac{1}{2}[/tex] r² = 2
→ Multiply both sides by 2
∴ r² = 4
→ Take √ for both sides
∴ r = 2
The height of the triangle is 8 meters and the radius of the semi-circle is 2 meters