Surface Area & Volume of a Right Pyramid

Surface Area of a Right Pyramid

A right pyramid is a solid 3D object with a base that is a regular polygon (all side lengths are the same), and with a vertex that is directly above the center of the base.

Surface Area

The surface area of a right pyramid can be broken down into the following:

• Area of the base Since this is a regular polygon, we can calculate the area by breaking it up into equal triangles
• Area of the triangular sides $\text{Each trigular side}=\dfrac{\text{Side length of polygon}\times\text{Slant height}}{2}$

To find the surface area, we add up the area of the base and the area of the triangular sides.

Square-Based Pyramid

The surface area of a square-based pyramid with base side length $b$ and a slant height of $L$ is

$\large\boxed{\text{S.A.}_\text{square-based pyramid}=b^2+2bL}$