Use the image to answer the question.

An illustration shows a triangle with sides measuring 21, 17, and 10. A perpendicular line, from the side measuring 21 to the opposite angle, measures 8. A right angle symbol is shown to the left of the perpendicular line.

A prism and a pyramid both have this triangular base. If both shapes have the same height and the volume of the prism is 1,092 cubic units, what is the volume of the pyramid?

(1 point)
Responses

728 cubic units
728 cubic units

364 cubic units
364 cubic units

3,276 cubic units
3,276 cubic units

1,092 cubic units
1,092 cubic units
Skip to navigation

1 answer

To find the volume of a pyramid that has the same base and height as a prism, we can use the relationship between the volumes of these two shapes.

The volume \( V \) of a prism is given by the formula: \[ V_{prism} = \text{Base Area} \times \text{Height} \]

The volume \( V \) of a pyramid is given by the formula: \[ V_{pyramid} = \frac{1}{3} \times \text{Base Area} \times \text{Height} \]

Since both shapes have the same base and height, we can relate the volumes as follows: \[ V_{pyramid} = \frac{1}{3} \times V_{prism} \]

Given that the volume of the prism is 1,092 cubic units: \[ V_{pyramid} = \frac{1}{3} \times 1,092 = 364 \text{ cubic units} \]

Thus, the volume of the pyramid is 364 cubic units.