Question

what is the volume of this triangular pyramid? 10 ft 16.7 ft 12.3 ft blank cubic feet submit

Explanation:

Step1: Find the area of the base triangle

The base of the triangular pyramid is a right triangle with legs \( 16.7 \, \text{ft} \) and \( 12.3 \, \text{ft} \). The area of a triangle is \( \frac{1}{2} \times \text{base} \times \text{height} \).
\[
\text{Base Area} = \frac{1}{2} \times 16.7 \times 12.3
\]
\[
\text{Base Area} = \frac{1}{2} \times 205.41 = 102.705 \, \text{square feet}
\]

Step2: Calculate the volume of the pyramid

The volume of a pyramid is \( \frac{1}{3} \times \text{Base Area} \times \text{Height} \), where the height of the pyramid is \( 10 \, \text{ft} \).
\[
\text{Volume} = \frac{1}{3} \times 102.705 \times 10
\]
\[
\text{Volume} = \frac{1027.05}{3} = 342.35 \, \text{cubic feet}
\]

Answer:

\( 342.35 \)