Question

find the surface area of a square pyramid with side length 1 in and slant height 2 in.

Explanation:

Step1: Calculate the base area

The base is a square with side length \(s = 1\) in. The area of the base \(B\) is \(B=s^{2}\).

$$B = 1^{2}=1\space\text{in}^{2}$$

Step2: Calculate the lateral surface area

The lateral surface area of a square - pyramid is \(LSA = 4\times(\frac{1}{2}\times s\times l)\), where \(s = 1\) in (side - length of the base) and \(l = 2\) in (slant height).

$$LSA=4\times(\frac{1}{2}\times1\times2)=4\space\text{in}^{2}$$

Step3: Calculate the total surface area

The total surface area \(SA\) of a square - pyramid is \(SA=B + LSA\).

$$SA=1 + 4=5\space\text{in}^{2}$$

Answer:

The surface area of the square pyramid is \(5\space\text{in}^{2}\)