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How to Find Volume and Surface Area of a Pyramid

Here you will learn to find the surface area and volume of a pyramid. A pyramid is a geometric figure that has a polygon as its base and as many side faces as the base has sides. The side faces are all triangles whose tops meet in a point.

Pyramid, square and four triangles

Surface Area

Rule

Surface Area of a Pyramid

Imagine that the pyramid is unfolded. The surface area is found by adding the area of the base and the areas of all the side faces.

Example 1

Find the surface area of a pyramid where the base is a square with sides of 5m. The height of the side faces of the pyramid is 6m.

First you need to find the area of the base surface:

Ab = 5m 5m = 25m2

Then you can find the area of the sides. Each side surface is a triangle with a base equal to 5 m and a height of 6 m:

As = 5 6 2 = 15m2

Since the base is a square, that is, a quadrilateral, you have four such triangles. The total surface area then becomes

A = Ab + 4 As = 25m2 + 4 15m2 = 85m2.

Volume

Formula

Volume of a Pyramid

V = B h 3 ,

where B is the area of the base, and h is the height of the pyramid.

Example 2

What is the volume of a pyramid that has a triangular base, where the triangle has a base of 4m and a height of 3m? The height of the pyramid is 5m.

First you need to calculate the area of the base: B = 4 3 2 = 6m2 V = 6 5 3 = 10m3

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