Question

1. the dimensions of the regular triangular pyramid are shown in the diagram. what is the volume of the pyramid in cubic inches?

Explanation:

Step1: Find base triangle area

The base is a triangle, use area formula: $\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}$
$\text{Base Area} = \frac{1}{2} \times 18 \times 14 = 126$ square inches

Step2: Apply pyramid volume formula

Volume of a pyramid is $\frac{1}{3} \times \text{base area} \times \text{height}$
$\text{Volume} = \frac{1}{3} \times 126 \times 16.5$

Step3: Calculate final volume

First compute $\frac{1}{3} \times 126 = 42$, then $42 \times 16.5 = 693$

Answer:

693 cubic inches