Question

Use the image to answer the question.

An illustration shows a triangle with sides measuring 16 meters, 14 meters, and 8 meters. A dashed perpendicular line, from the side measuring 16 meters to the opposite angle, measures 7 meters. A right angle symbol is shown to the left of the perpendicular line.

A prism and pyramid have congruent triangular bases. If their heights are both 15 m, what is the volume of each shape?

(1 point)
The volume of the prism is
m3.
The volume of the pyramid is
m3.
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Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the volume of the prism and pyramid with congruent triangular bases, we need to calculate the area of the base first. The area of a triangle can be calculated using the formula A = 1/2 * base * height.

For the prism:
Base area = 1/2 * 16m * 7m = 56 m^2
Volume of the prism = Base area * height = 56 m^2 * 15 m = 840 m^3

For the pyramid:
Base area = 1/2 * 16m * 7m = 56 m^2
Volume of the pyramid = (1/3) * Base area * height = (1/3) * 56 m^2 * 15 m = 280 m^3

Therefore, the volume of the prism is 840 m^3 and the volume of the pyramid is 280 m^3.