Question

find the surface area of a square pyramid with side length 1 km and slant height 3 km.

Explanation:

Step1: Calculate the base area

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

$$B = 1^{2}=1$$

Step2: Calculate the lateral surface area

The lateral surface area of a square - pyramid is \(LSA = 2sl\), where \(s\) is the side length of the base and \(l\) is the slant height. Here, \(s = 1\) km and \(l=3\) km.

$$LSA=2\times1\times3 = 6$$

Step3: Calculate the total surface area

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

$$SA=1 + 6=7$$

Answer:

\(7\)