How to find the surface area of a prism?

Steps to Solve

1. Identify the shape of the bases

The first step is to determine the shape of the bases of the prism. For example, if it's a rectangular prism, the bases will be rectangles. Knowing the shape helps in calculating the area of the bases.

2. Calculate the area of one base

Use the appropriate formula for the area of the shape of the base. For example, if it's a rectangle, use the formula $A = l \times w$, where $l$ is the length and $w$ is the width.

3. Multiply the area of the base by 2

Since a prism has two congruent bases, multiply the area of one base by 2 to get the total area of both bases:

$$A_{bases} = 2 \times ( \text{area of one base} )$$

4. Calculate the perimeter of the base

Calculate the perimeter of one of the bases. For a rectangle, the perimeter $P$ is given by: $$P = 2(l+w)$$.

5. Calculate the lateral surface area

The lateral surface area is given by the product of the perimeter of the base and the height $h$ of the prism:

$$A_{lateral} = P \times h$$

6. Sum the areas of the bases and the lateral faces

Add the total area of the bases to the lateral surface area to get the surface area of the prism:

$$A_{surface} = A_{bases} + A_{lateral}$$