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.
The volume of a prism is calculated by multiplying the area of the base by the height of the prism. Since the base is a triangle with sides 16, 14, and 8 meters, we can calculate the area using Heron's formula:
s = (16 + 14 + 8) / 2 = 19 meters (semiperimeter)
Area = √(19(19-16)(19-14)(19-8)) = √(19*3*5*11) = √3135 ≈ 56.02 m^2
Volume of the prism = 56.02 m^2 * 15 m = 840.3 m^3
The volume of a pyramid is calculated by taking 1/3 of the volume of a prism with the same base and height. Therefore:
Volume of the pyramid = 1/3 * 840.3 m^3 = 280.1 m^3
Therefore, the volume of the prism is 840.3 m^3 and the volume of the pyramid is 280.1 m^3.