Question

Find the lateral surface area, total surface area and volume of a square pyramid with base edge length 24 cm, and height 16 cm.

Answer 1

Given:
Base edge length = 24 cm
Height = 16 cm
We know that,

${\text{(Slant height)}}^2={\text{(Height)}}^2+(\frac{\text{Base edge}}{2}{)}^2$

$\text{Slant height}=\sqrt{{16}^2+{12}^2}=20cm$

Therefore,
Lateral surface area of the square pyramid = area of four triangles
$=4\times (\frac{1}{2}\times baseedge\times slantheight)$
$=4\times (\frac{1}{2}\times 24\times 20)$
$=960c{m}^2$

Total surface area of the square pyramid = Area of the square + Lateral surface area
$=(\text{base edge}\times \text{base edge})+960$
$=(24\times 24)+960$
$=576+960$
$=1536c{m}^2$

Now,
Volume of the square pyramid
$=\frac{1}{3}\times \text{base area}\times \text{Height}$
$\frac{1}{3}\times (24\times 24)\times 16$
$=3072c{m}^3$