Answer:
Step-by-step explanation:
The formula of a volume of a prism:
[tex]V=A_BH[/tex]
[tex]A_B-area\ of\ a\ base\\H-height[/tex]
We have
[tex]V=72\ ft^3,\ H=9\ ft[/tex]
Substitute:
[tex]72=9A_B[/tex] divide both sides by 9
[tex]8=A_B\to A_B=8\ ft^2[/tex]
The area of the triangular base of the given prism with a volume of 72 cubic feet and a height of 9 feet is 8 sq. feet. It is calculated by using the volume of a prism formula.
The volume of the prism with a base area and height is given as
Volume = Area of the base of the prism × height of the prism
i.e., V = [tex]B_a[/tex] × h
Here the base of the prism is an isosceles right triangle. So, the volume is given by
V = Area of isosceles right triangle × height of the prism
Given that volume of the prism is 72 cubic feet and the height of the prism is 9 feet.
Thus, the area of the triangular base is calculated as follows:
V = Area of triangular base × height of the prism
⇒ Area of the triangular base = Volume/height of the prism
⇒ Area of the triangular base = [tex]\frac{72}{9}[/tex]
∴ Area of the triangular base = 8 sq. feet
Therefore, the area of the triangular base for the given right triangular prism is 8 sq. feet
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