Question

find the volume of the triangular pyramid given the measures shown. note that the figure is not to scale.

Explanation:

Step1: Find the area of the base triangle

The base of the triangular pyramid is a right triangle with legs 3 and 4. The area of a triangle is given by \( A=\frac{1}{2}\times base\times height \). So, the area of the base \( B=\frac{1}{2}\times3\times4 \).
\( B = 6 \)

Step2: Use the volume formula for a pyramid

The volume \( V \) of a pyramid is given by \( V=\frac{1}{3}\times B\times h \), where \( B \) is the area of the base and \( h \) is the height of the pyramid. Here, \( B = 6 \) and \( h = 6 \).
So, \( V=\frac{1}{3}\times6\times6 \)

Step3: Calculate the volume

\( \frac{1}{3}\times6\times6= 12 \)

Answer:

The volume of the triangular pyramid is 12.