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 is a right triangle with legs 2 and 6. The area of a triangle is $\frac{1}{2} \times base \times height$. So, the area of the base $B = \frac{1}{2} \times 2 \times 6$.
$B = \frac{1}{2} \times 12 = 6$

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 $h = 7$.
So, $V = \frac{1}{3} \times 6 \times 7$

Step3: Calculate the volume

First, $\frac{1}{3} \times 6 = 2$. Then, $2 \times 7 = 14$.

Answer:

14