# How to find the surface area of a square pyramid?

#### Understand the Problem

The question is asking for the method to calculate the surface area of a square pyramid, which involves understanding the formulas for area of both the square base and the triangular faces.

Total Surface Area

The final answer is the Total Surface Area

#### Steps to Solve

1. Calculate the area of the square base

The area of the square base can be found using the formula:

$$ext{Area}_{ ext{base}} = s^2$$

where $s$ is the length of a side of the square base.

1. Calculate the area of one triangular face

The triangular faces are isosceles triangles. The area of one triangle can be calculated using the formula:

$$ext{Area}_{ ext{triangle}} = rac{1}{2} imes ext{base} imes ext{height}$$

The base of one triangle is $s$, and the height can be found using the Pythagorean theorem if the slant height $l$ is known:

$$ext{height}_{ ext{triangle}} = rac{l^2 - rac{s^2}{4}}{s}$$

1. Calculate the area of four triangular faces

After finding the area of one triangular face, multiply it by 4 to get the total area of the triangular faces:

$$ext{Area}{ ext{triangles}} = 4 imes ext{Area}{ ext{triangle}}$$

Finally, add the area of the square base and the total area of the triangular faces to find the total surface area:

$$ext{Surface area} = ext{Area}{ ext{base}} + ext{Area}{ ext{triangles}}$$

The final answer is the Total Surface Area