How to find the surface area of a prism?
Understand the Problem
The question is asking for the method to calculate the surface area of a prism, which involves summing the areas of all the faces of the prism. This typically includes calculating the areas of the two bases and the lateral faces.
Answer
Calculate the individual areas of the bases and the lateral faces, then sum them.
Answer for screen readers
The surface area of a prism can be calculated by summing the areas of all its faces.
Steps to Solve
- 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.
- 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.
- 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:
$$A_{bases} = 2 \times ( \text{area of one base} )$$
- Calculate the perimeter of the base
Calculate the perimeter of one of the bases. For a rectangle, the perimeter $P$ is given by: $$P = 2(l+w)$$.
- 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:
$$A_{lateral} = P \times h$$
- 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:
$$A_{surface} = A_{bases} + A_{lateral}$$
The surface area of a prism can be calculated by summing the areas of all its faces.
More Information
The method for calculating the surface area of a prism depends heavily on knowing the shape of its base and its dimensions.
Tips
A common mistake is forgetting to double the area of the base, as there are two identical bases in a prism.