Question

Find lateral surface area and volume for 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$$\left[1mark\right]$

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$$\left[1mark\right]$