Question

the volume of a right triangular prism is 72 cubic feet. the height of the prism is 9 feet. the triangular base is an isosceles right triangle. what is the area of the triangular base? square feet what is the length of edge df? feet

Explanation:

Step1: Recall volume formula for prism

The volume formula for a prism is $V = Bh$, where $V$ is the volume, $B$ is the area of the base, and $h$ is the height of the prism.

Step2: Calculate the area of the base

We know that $V = 72$ cubic - feet and $h=9$ feet. Substituting these values into the formula $V = Bh$, we get $72=B\times9$. Solving for $B$, we divide both sides of the equation by 9: $B=\frac{72}{9}=8$ square - feet.

Step3: Recall area formula for isosceles right - triangle

The area formula for a right - triangle is $A=\frac{1}{2}s^{2}$, where $s$ is the length of a leg of the right - triangle. Since the base is an isosceles right - triangle and $A = B=8$ square feet, we have $8=\frac{1}{2}s^{2}$.

Step4: Solve for the side length

Multiply both sides of the equation $8=\frac{1}{2}s^{2}$ by 2 to get $16 = s^{2}$. Then take the square root of both sides. Since $s>0$, we have $s = 4$ feet. Let the leg of the isosceles right - triangle base be $DF$, so the length of $DF$ is 4 feet.

Answer:

The area of the triangular base is 8 square feet.
The length of edge $DF$ is 4 feet.