Question

determine the volume of the three-dimensional figure.

the volume of the three-dimensional figure is \text{____} \text{m}^3.
(type an integer or decimal.)

Explanation:

Identify the shape and dimensions

The given figure is a triangular prism. The base of the prism is a right-angled triangle, and the length of the prism connects the two triangular bases.

• Base of the right triangle: \(b = 8\text{ m}\)
• Height of the right triangle: \(h = 8\text{ m}\)
• Length (height) of the prism: \(L = 15\text{ m}\)

Calculate the area of the triangular base

Using the Triangle Area knowledge point

$$ \text{Area}_{\text{base}} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 8\text{ m} \times 8\text{ m} = 32\text{ m}^2 $$

Calculate the volume of the prism

Using the Volume of Prism knowledge point

$$ V = \text{Area}_{\text{base}} \times L = 32\text{ m}^2 \times 15\text{ m} = 480\text{ m}^3 $$

Answer:

Determine the volume of the three-dimensional figure.

The volume of the three-dimensional figure is <blank>480</blank> \(\text{m}^3\).