Question

what is the volume of this triangular pyramid? 10.7 in 17.4 in 18 in cubic inches

Explanation:

Step1: Calculate the base area

The base is a triangle with base \(b = 18\) in and height \(h_{base}=17.4\) in. The area of a triangle \(A=\frac{1}{2}\times b\times h_{base}\).

$$A=\frac{1}{2}\times18\times17.4 = 9\times17.4=156.6$$

Step2: Calculate the volume of the pyramid

The volume of a pyramid \(V=\frac{1}{3}\times A\times H\), where \(A\) is the base - area and \(H = 10.7\) in is the height of the pyramid.

$$V=\frac{1}{3}\times156.6\times10.7$$

$$V = 52.2\times10.7$$

$$V=558.54$$

Answer:

\(558.54\)