# Surface Area of a Square Pyramid

## Online Tutoring Is The Easiest, Most Cost-Effective Way For Students To Get The Help They Need Whenever They Need It.

#### SIGN UP FOR A FREE TRIAL

A square pyramid is a 3-dimensional geometric figure consisting of a base and 4 triangles. These 4 triangles of the pyramid join the base to a single point on top known as the ‘apex’ or the ‘vertex’ of the pyramid. A pyramid can have different bases, but the pyramid having a square base is known as the ‘square pyramid’. Surface area of a square pyramid can be calculated by finding the sum of the area of the base and the areas of the 4 triangles together.

Example 1: What is the surface area of a square pyramid which has a base length of 5m and a slant height of 12m?

Given: base length, b= 5m

Slant height of the pyramid, s = 12m

Since it is a square pyramid, the base of the pyramid is a square.

Surface area of a square pyramid = b2 + 2* b* s

This gives: Surface area of the square pyramid, SA= (5)2 + (2 * 5 * 12) = 25+ 120= 145m2

Therefore, the surface area of the given square pyramid is 145m2

Example 2: What is the surface area of a square pyramid which has a base length of 7m and a slant height of 11m?

Given: base length, b= 7m

Slant height of the pyramid, s = 11m

Since it is a square pyramid, the base of the pyramid is a square.

Surface area of a square pyramid = b2 + 2* b* s

This gives: Surface area of the square pyramid, SA= (7)2 + (2 * 7 * 11) = 49+ 154= 203m2

Therefore, the surface area of the given square pyramid is 203m2