Calculate Total Surface Area of a Square Pyramid

Consider a pyramid with a square base of side length 6 cm and a height of 10 cm. What is the total surface area of the pyramid?

To find the total surface area of a square pyramid, use the formula:

$$ ext{Total Surface Area} = ext{Base Area} + ext{Lateral Surface Area}$$

The base area is calculated as follows:

$$ ext{Base Area} = s^2$$

where $s$ is the side length of the base. The lateral surface area can be calculated using:

$$ ext{Lateral Surface Area} =\frac{1}{2} imes ext{perimeter of base} imes ext{slant height}$$

The slant height $l$ can be determined using the Pythagorean theorem:

$$l = ext{sqrt} igg( igg(\frac{s}{2} igg)^2 + h^2 igg)$$

where $h$ is the height of the pyramid.