The image shows a sheet of paper with a diagram of a triangular prism. The diagram includes measurements indicating a height of 9 ft, a base length of 16 ft, and a side length of 4 ft. The text on the paper asks for the volume of the triangular prism, with multiple-choice options provided: A) 576 ft3, B) 288 ft3, C) 34 ft3, D) 29 ft3

Answer 1

To find the volume of the triangular prism, we can use the formula:

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

The base of the prism is a triangle. The area of a triangle can be calculated using the formula:

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

In this case, the base of the triangle is given as 16 ft, and the height as 4 ft (side length from the right angle of the triangle to the base). So the area of the triangle is:

\[ \text{Area} = \frac{1}{2} \times 16 , \text{ft} \times 4 , \text{ft} = \frac{1}{2} \times 64 , \text{ft}^2 = 32 , \text{ft}^2 \]

Now, using the area of the triangle to calculate the volume of the prism:

\[ \text{Volume} = \text{Base Area} \times \text{Height} = 32 , \text{ft}^2 \times 9 , \text{ft} = 288 , \text{ft}^3 \]

Thus, the volume of the triangular prism is \(288 , \text{ft}^3\).

The correct answer is B) 288 ft³.