Question

a terrarium is built in the shape of a triangular prism. the prism is 10 inches in height and contains 450 cubic inches of space. what is the area of the base shape of the prism? square inches 10 22.5 45

Explanation:

Step1: Recall prism volume formula

The volume \( V \) of a prism is \( V = B \times h \), where \( B \) is the area of the base, and \( h \) is the height of the prism.

Step2: Rearrange to solve for \( B \)

Isolate \( B \) by dividing both sides by \( h \):
\( B = \frac{V}{h} \)

Step3: Substitute given values

Substitute \( V = 450 \) cubic inches and \( h = 10 \) inches:
\( B = \frac{450}{10} = 45 \)

Answer:

45 square inches