Question

8)

volume =

5.9 in
7.1 in
4.2 in

Explanation:

Identify the given dimensions

We have a triangular prism.
The triangular base has:

• Base length \(b = 7.1\text{ in}\)
• Height \(h = 4.2\text{ in}\)

The length (or height) of the prism is:

• \(L = 5.9\text{ in}\)

Calculate base area

Find the area of the triangular base.

$$ B = \frac{1}{2} \times b \times h $$

$$ B = \frac{1}{2} \times 7.1 \times 4.2 = 14.91\text{ in}^2 $$

Calculate the volume

Multiply base area by prism length.

$$ V = B \times L $$

$$ V = 14.91 \times 5.9 = 87.969\text{ in}^3 $$

Round the final value

Round to two decimal places.

$$ V \approx 87.97\text{ in}^3 $$

Answer:

Volume = <blank>\(87.97\text{ in}^3\)</blank>