Question

find the surface area of a square pyramid with side length 3km and slant height 5km

Answer 1

$\text{ 36 }km^2$

Explanation

the surface area of a square pyramid is given by:

$\begin{gathered} sa=A+\frac{1}{2}ps \\ \text{where A is the area of the base} \\ p\text{ is the perimeter of the base} \\ s\text{ is the }slant\text{ heigth} \end{gathered}$

so

Step 1

area of the base

the baseis a square, so the area is

$\begin{gathered} Area=side^{^2} \\ Area_{base}=3km\cdot\text{ 3}km \\ Area_{base}=\text{ 9(}km^2) \end{gathered}$

Step 2

perimeter of the base

the perimeter of a square is given by:

$\begin{gathered} \text{Perimeter}=\text{ 4}\cdot side \\ sp \\ \text{Perimeter}=\text{ 4}\cdot3km\text{ =12 }km \\ \text{Perimeter}=12km \end{gathered}$

Step 3

finally, let

$\text{slant heigth=5}km$

now, replace in the formula

$\begin{gathered} sa=A+\frac{1}{2}ps \\ sa=9(km^2)+\frac{1}{2}(12km)(5km) \\ sa=9(km^2)+30(km^2) \\ sa=39(km^2) \end{gathered}$

therefore, the answer is

$\text{ 36 }km^2$

I hope this helps you