Question

what is the volume of this triangular pyramid? 6 ft, 8 ft, 10.5 ft, cubic feet, submit

Explanation:

Step1: Find the area of the triangular base

The base of the triangular pyramid is a triangle with base \( b = 10.5 \) ft and height \( h_{base}= 6 \) ft. The area of a triangle is given by \( A=\frac{1}{2}\times b\times h \). So, the area of the base \( A=\frac{1}{2}\times10.5\times6 \).
\[

$$\begin{align*} A&=\frac{1}{2}\times10.5\times6\\ & = 10.5\times3\\ &= 31.5 \end{align*}$$

\]

Step2: Use the volume formula for a pyramid

The volume \( V \) of a pyramid is given by \( V=\frac{1}{3}\times A\times h_{pyramid} \), where \( A \) is the area of the base and \( h_{pyramid} = 8 \) ft (the height of the pyramid). Substituting \( A = 31.5 \) and \( h_{pyramid}=8 \) into the formula:
\[

$$\begin{align*} V&=\frac{1}{3}\times31.5\times8\\ & = 10.5\times8\\ &= 84 \end{align*}$$

\]

Answer:

84