# 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).

\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:

$$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$

#### Steps to Solve

1. 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.

1. 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.
1. 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: $$\text{Lateral Area} = \frac{1}{2} \times \text{Perimeter of Base} \times \text{Slant Height}$$

1. 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:

$$\text{Surface Area} = \text{Base Area} + \text{Lateral Area}$$