How do you find the surface area of a pyramid?
Understand the Problem
The question is asking how to calculate the surface area of a pyramid, which generally involves using the formula for the lateral area plus the base area depending on the specific type of pyramid (e.g., square-based, triangular-based).
Answer
\text{Surface Area} = \text{Base Area} + \text{Lateral Area}
Answer for screen readers
The surface area of a pyramid is the sum of the base area and the lateral area, which is given by:
$$ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} $$
Steps to Solve
- Identify the pyramid type and its dimensions
Identify if the pyramid has a square, rectangular, or triangular base. Note down the dimensions: the side length(s) of the base and the slant height of the pyramid.
- Calculate the base area
Calculate the area of the base of the pyramid using the appropriate formula for the shape:
- For a square base: $ ext{Base Area} = s^2 $ where $ s $ is the side length.
- For a rectangular base: $ ext{Base Area} = l imes w $ where $ l $ and $ w $ are the length and width.
- For a triangular base: $ ext{Base Area} = \frac{1}{2} \times b \times h_b $ where $ b $ is the base length and $ h_b $ is the height of the triangle.
- Calculate the lateral area
The lateral area is the sum of the areas of all the triangular faces. For a pyramid with a square or rectangular base, you can calculate the area of one triangular face and multiply by the number of faces: $$ \text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of Base} \times \text{Slant Height} $$
- Calculate the surface area
Add the base area and the lateral area to get the total surface area: $$ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} $$
The surface area of a pyramid is the sum of the base area and the lateral area, which is given by:
$$ \text{Surface Area} = \text{Base Area} + \text{Lateral Area} $$
More Information
This formula applies to any type of pyramid. Just ensure you accurately calculate the base and lateral areas according to the pyramid's specific dimensions.
Tips
A common mistake is confusing slant height with vertical height. Ensure you distinguish between the two as they are different measurements.