Question

The base of the right triangular prism is a right triangle with legs that measure 5 cm and 8 cm. If the height of the prism is 12 cm, what is the volume, V, of the prism?

Answer 1

it's wrong

Answer 2

To find the volume of a right triangular prism, you can use the formula:
V = (1/2) * b * h * l
where b is the base of the right triangle, h is the height of the prism, and l is the length of the prism.

In this case, the base of the right triangle has legs that measure 5 cm and 8 cm, so the area of the base is:
(1/2) * 5 * 8 = 20 cm²

The height of the prism is 12 cm.

The length of the prism can be found using the Pythagorean theorem:
l = √(5² + 8²) = √(25 + 64) = √89 ≈ 9.43 cm

Now, plug in the values into the formula:
V = (1/2) * 20 * 12 * 9.43
V = 120 * 9.43
V ≈ 1131.6 cm³

Therefore, the volume of the right triangular prism is approximately 1131.6 cm³.

Answer 3

I apologize for the mistake. Let's try to re-calculate the volume of the right triangular prism.

The base area of the right triangle can be calculated as:
(1/2) * 5 * 8 = 20 square cm

The height of the prism is given as 12 cm and the area of the base is 20 square cm.

Therefore, the volume of the right triangular prism is:
V = base area * height
V = 20 * 12
V = 240 cubic cm

Therefore, the volume of the right triangular prism is 240 cubic cm.