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Question

Find the surface area and volume of a rectangular pyramid.


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Solution

Step 1: Definition of rectangular pyramid:

Pyramids are three-dimensional structures having triangle faces and have an encompassing polygon shape at their base.

A rectangular pyramid is simply a pyramid with a base that is a rectangle.

V=The volume of the rectangular pyramid

A=The total surface area of the rectangular pyramid

L=Length of the base

B=Width of the base

H=Height of the pyramid

l=Slant height of the pyramid

Step 2: Solve for surface area of pyramid

The Lateral surface area of a rectangular pyramid is

LSA=12×Perimeter of base × Slant height

We know that perimeter of rectangle =2L+B

Slant height l=H2+L22

LSA=12×2L+B×H2+L22

LSA=L+B×H2+L22

Area of base A'=L×B

A=LSA+A'

A=L+B×H2+L22+L×B

Step 3: Solve for volume of the pyramid

The volume of the rectangular pyramid V=13× Area of base × Height of the pyramid

V=13×A'×HV=L×B×H3

Hence, the surface area and volume of the rectangular pyramid are L+B×H2+L22+L×B and L×B×H3 respectively


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