Question

find the surface area of a square pyramid with side length 2 km and slant height 4 km

Answer 1

The diagram can be drawn as,

The surface area of the base is

$\begin{gathered} BA=(2km)^2 \\ ^{}=4\text{ sq. km} \end{gathered}$

The lateral surface area can be determined as,

$\begin{gathered} \text{LSA}=\frac{1}{2}\times Perimeter\text{ of base}\times slant\text{ height} \\ =\frac{1}{2}\times(4\times2\text{ km)}\times4\text{ km} \\ =16\text{ sq km.} \end{gathered}$

The total surface area can be determined as,

$\begin{gathered} \text{TSA}=BA+\text{LSA} \\ =4\text{ sq km+16 sq km} \\ =20\text{ sq km.} \end{gathered}$

Thus, the total surface area is 20 sq km.