Question

what is the volume of this triangular pyramid? cubic inches

Explanation:

Step1: Find the area of the triangular base

The base of the triangular pyramid is a right triangle with legs 36 in and 38 in. The area of a triangle is given by \( A=\frac{1}{2}\times base\times height \). So, \( A = \frac{1}{2}\times36\times38 \)
\( A=\frac{1}{2}\times1368 = 684 \) square inches.

Step2: Use the volume formula for a pyramid

The volume of a pyramid is \( V=\frac{1}{3}\times base\ area\times height \). Here, the height of the pyramid (the perpendicular height from the apex to the base) is 34 in. So, \( V=\frac{1}{3}\times684\times34 \)
First, calculate \( \frac{1}{3}\times684 = 228 \). Then, \( 228\times34 = 7752 \)

Answer:

7752