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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To find the volume of the prism, we first need to find the area of the triangle base. Using Heron's formula, we can calculate the area as follows:
s = (16 + 14 + 8) / 2 = 19
Area = √(19(19-16)(19-14)(19-8)) = √(19*3*5*11) = √3135 ≈ 56.01 m^2
Now, we can find the volume of the prism:
Volume = Base area * height = 56.01 * 15 = 840.15 m^3
Similarly, the volume of the pyramid with the same triangular base area and height would be:
Volume = (1/3) * Base area * height = (1/3) * 56.01 * 15 = 280.05 m^3
Therefore, the volume of the prism is 840.15 m^3 and the volume of the pyramid is 280.05 m^3.