To calculate the volume of the prism, we first need to calculate the area of the base triangle. Using Heron's formula:
S = (16 + 14 + 8) / 2 = 19
Area = sqrt(19 * (19-16) * (19-14) * (19-8)) = sqrt(19 * 3 * 5 * 11) = sqrt(3135) ≈ 56.01 m^2
Now, the volume of the prism is calculated as the area of the base triangle multiplied by the height:
Volume = 56.01 * 15 = 840.15 m^3
The volume of the prism is 840.15 m^3.
Since the pyramid and prism have congruent bases, the volume of the pyramid is 1/3 of the volume of the prism. Therefore, the volume of the pyramid is:
Volume = 1/3 * 840.15 = 280.05 m^3
The volume of the pyramid is 280.05 m^3.
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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.
1 answer