Question

Find the volume of the triangular pyramid below. Round your answer to the nearest tenth if necessary.
10 hiegth
8 width
11 length

Answer 1

To find the volume of a triangular pyramid (also known as a tetrahedron), we use the formula:

\[
\text{Volume} = \frac{1}{3} \times \text{Base Area} \times \text{Height}
\]

In this case, we need to first calculate the area of the triangular base. The base of the pyramid is a triangle, and if we assume the dimensions given (width and length) represent the two sides of the triangle (base and height respectively), then we can calculate the area of the triangle using the formula:

\[
\text{Base Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]

Assuming the width (8) is the base and the length (11) is the height of the triangle, we can calculate the base area:

\[
\text{Base Area} = \frac{1}{2} \times 8 \times 11 = \frac{88}{2} = 44
\]

Now, we can substitute this value back into the volume formula along with the height of the pyramid (10):

\[
\text{Volume} = \frac{1}{3} \times 44 \times 10 = \frac{440}{3} \approx 146.67
\]

Rounding to the nearest tenth, we find:

\[
\text{Volume} \approx 146.7
\]

Thus, the volume of the triangular pyramid is approximately **146.7 cubic units**.