The height of the pyramid is 7 yards.
Given that, the volume of a pyramid is 84 cubic yards and the base area is 36 square yards.
We need to find what is the height of the pyramid.
Let us consider a pyramid and prism each of which has a base area 'B' and height 'h'. We know that the volume of a prism is obtained by multiplying its base by its height. i.e., the volume of the prism is Bh. In the earlier section, we have seen that the volume of the pyramid is one-third of the volume of the corresponding prism (i.e., their bases and heights are congruent). Thus,
The volume of the pyramid = (1/3)(Bh), where
B = Area of the base of the pyramid
h = Height of the pyramid
Now, the volume of the pyramid = (1/3)(36 × h)
⇒84=12× h
⇒h=7 yards
Therefore, the height of the pyramid is 7 yards.
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