How to find the surface area of a right prism?
Understand the Problem
The question is asking how to calculate the surface area of a right prism, which involves using the formula for surface area based on the base shape and the height of the prism.
Answer
The surface area of a right prism is given by \( S = 2B + L \).
Answer for screen readers
The total surface area of the right prism ( S ) is given by: $$ S = 2B + L $$
Steps to Solve
- Identify the base shape and base area
Determine the shape of the base of the right prism (for instance, triangle, rectangle, or other polygon) and calculate the area of this base. If the base shape is a rectangle with length ( l ) and width ( w ), the area ( A ) is given by: $$ A = l \times w $$
- Determine the height of the prism
Identify the height ( h ) of the prism, which is the distance between the two bases.
- Calculate the lateral surface area
The lateral surface area ( L ) is found by multiplying the perimeter ( P ) of the base by the height ( h ): $$ L = P \times h $$
- Find the total surface area
Combine the base area and lateral surface area to find the total surface area ( S ) of the prism. If ( B ) is the area of the base, the total surface area is: $$ S = 2B + L $$
- Substitute values and simplify
Substitute the known values into the equations and simplify to find the total surface area.
The total surface area of the right prism ( S ) is given by: $$ S = 2B + L $$
More Information
The formula for the surface area of a right prism allows for calculation based on the shape of the base and the height, making it versatile for various base shapes.
Tips
- Forgetting to consider both bases when calculating surface area.
- Confusing perimeter with area, especially when calculating the lateral surface area. Always use the correct units for area and linear measurements.
- Neglecting to include the height in the lateral surface area calculation.
