Finding Lateral Surface Area

Property We can find the lateral surface area of prisms and cylinders by multiplying the perimeter or circumference of the base by the height. $$ \text{Lateral surface area} = \text{perimeter of base} \cdot \text{height} $$.

Examples A cube with 8 cm edges has a base perimeter of $4 \times 8 = 32 \text{ cm}$. Lateral area is $32 \text{ cm} \times 8 \text{ cm} = 256 \text{ cm}^2$. A building with a base perimeter of 120 ft and height of 15 ft has a lateral area of $120 \text{ ft} \times 15 \text{ ft} = 1800 \text{ ft}^2$. A tissue box is 9 in by 5 in at the base. Its perimeter is $2(9+5)=28 \text{ in}$. With a height of 4 in, the lateral area is $28 \text{ in} \times 4 \text{ in} = 112 \text{ in}^2$.

Explanation Imagine peeling the label off a soup can. When you lay it flat, it becomes a rectangle! The rectangle's height is the can’s height, and its length is the circle's circumference. This same cool trick works for the sides of a prism; it is just the base's perimeter multiplied by the object's height.