How to Find the Lateral Area of a Square Pyramid

How to Find the Lateral Area of a Square Pyramid
••• sculpies/iStock/GettyImages

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.

Related Articles

Characteristics of Rectangular Pyramids
What Is a Compound Shape?
How to Calculate the Area of a Cube
How to Calculate Pyramid Angles
How to Find the Total Surface Area of a Closed Cylinder
How to Find the Volume of a Triangular Pyramid
The Properties of a Triangular-Based Pyramid
Properties of a Triangular Pyramid
How to Calculate the Area of a Base
How to Calculate the Volume of a Triangle
How to Calculate Volume of a Circular Cylinder
How to Find the Surface Area of a Hexagonal Prism
How to Find the Missing Slope of a Trapezoid
How to Calculate Quadrilateral Area
How to Calculate Area of a Triangle
What Are Prisms & Pyramids?
Formula for the Volume of a Octagon
How to Calculate the Length of Octagon Sides
How to Calculate Shear Area
How to Convert Square Dimensions to Round

Dont Go!

We Have More Great Sciencing Articles!