Answer:
The volume of the given figure is 150 mm³
Step-by-step explanation:
The formula of the volume of the triangular pyramid is V = [tex]\frac{1}{3}[/tex] AH, where
- A is the area of its base
The formula of the area of a triangle is A = [tex]\frac{1}{2}[/tex] bh, where
- b is the length of its base
- h is the length of its height
In the given figure
∵ The pyramid has a triangular base
∵ The triangle has a base of 12 mm and a height of 7.5 mm
∴ b = 12 mm and h = 7.5 mm
→ By using the 2nd formula above, find the area of the base
∴ A = [tex]\frac{1}{2}[/tex] (12)(7.5)
∴ A = 45 mm²
∵ The height of the pyramid is 10 mm
∴ H = 10 mm
∵ A = 45 mm²
→ Substitute them in the first formula above to find the volume
∴ V = [tex]\frac{1}{3}[/tex] (45)(10)
∴ V = 150 mm³
∴ The volume of the given figure is 150 mm³
