Question

what is the volume of this triangular pyramid? 10 mm 13.5 mm 7 mm cubic millimeters

Explanation:

Step1: Find the area of the base triangle

The base is a right triangle with legs 10 mm and 13.5 mm. The area of a triangle is $\frac{1}{2} \times base \times height$. So, the area of the base $B = \frac{1}{2} \times 10 \times 13.5 = 67.5$ square millimeters.

Step2: Use the volume formula for a pyramid

The volume of a pyramid is $V = \frac{1}{3} \times B \times h$, where $h$ is the height of the pyramid (7 mm here). Substitute $B = 67.5$ and $h = 7$ into the formula: $V = \frac{1}{3} \times 67.5 \times 7$.

Step3: Calculate the volume

First, $\frac{1}{3} \times 67.5 = 22.5$. Then, $22.5 \times 7 = 157.5$.

Answer:

157.5