Question

Find the lateral surface area, total surface area and volume of a square pyramid with the following specification: a = base edge length, h = slant height and H = height.

Answer 1

$\text{Volume of pyramid}=\frac{1}{3}\times \text{base area}\times \text{height}$
$=\frac{1}{3}\times (a\times a)\times H$
$=\frac{1}{3}{a}^{2}H$

$\text{Lateral surface area of pyramid}$
$=\text{area of four triangles}$
$=4\times (\frac{1}{2}\times \text{base edge}\times \text{slant height})$
$=2\times \text{base edge}\times \text{slant height}$
$=2ah$

$\text{Total surface area of the pyramid}$
$=(\text{base edge}{)}^2+\text{lateral surface area}$
$=a^2+2ah$