# How to Find the Lateral Area of a Square Pyramid

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Math problems involving three-dimensional shapes may require you to find the lateral surface area of a square pyramid. The lateral surface area is the sum of the areas of its lateral faces (sides), while the total surface area is the sum of its lateral faces and its base. So in a square pyramid, the lateral faces are the four triangles that form the top and side portions of the shape. The general formula for the lateral surface area of a regular pyramid is

\text{lateral area} = \frac{\text{ perimeter of base} × \text{ slant height of pyramid}}{2}

Calculate the perimeter of the base by multiplying the length of one edge by four because a square has four equal sides. For example, if the side of a square pyramid measures 6 inches, the perimeter is

4 × 6 = 24 \text{ inches}

The lateral slant height is the distance from the top of the pyramid to the edge of the base that bisects one of the triangle faces. If the lateral slant height is 8 inches, work out

24 × 8 = 192

To find the lateral surface area, work out

\frac{192}{2} = 96

You now know that the lateral surface area of a square pyramid with a base perimeter of 24 inches and a lateral slant height of 8 inches is 96 square inches.

#### Tips

• If you already know the area of each of the four lateral faces of a square pyramid, you can work out the lateral surface area by finding the sum of areas of the lateral faces. For example, if the areas of the lateral faces are 10 inches, 10 inches, 7 inches and 7 inches, work out 10 + 10 + 7 + 7 = 34. The lateral surface area is 34 square inches.