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
3,276 cubic units
3,276 cubic units
1,092 cubic units
1,092 cubic units
364 cubic units
364 cubic units
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To find the volume of the pyramid with the same base and height as the prism, we can use the formula for the volume of a pyramid, which is 1/3 * base area * height.
First, we need to find the area of the base triangle. We can use Heron's formula to calculate the area:
s = (21 + 17 + 10) / 2 = 24
Area = sqrt(24 * (24 - 21) * (24 - 17) * (24 - 10)) = sqrt(24 * 3 * 7 * 14) = sqrt(7056) = 84
Now, we can calculate the volume of the pyramid:
Volume = 1/3 * 84 * 8 = 224
Therefore, the volume of the pyramid is 224 cubic units.