Question

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

Answer 1

`\text{ 36 }km^2`

Step-by-step explanation

the surface area of a square pyramid is given by:

`\begin{gathered} sa=A+(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+(1)/(2)ps \\ sa=9(km^2)+(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