Question

A tent in the form of a square pyramid has a height of 12 cm and the base edge length is 18 cm. Find the total cloth required to build the tent.

• A. $834c{m}^2$
• B. $324c{m}^2$
• C. $510c{m}^2$
• D. $540c{m}^2$

Answer 1

The correct option is D

$540c{m}^2$

Given that,
Height of the pyramid = 12 cm
Base edge of the pyramid = 18 cm
Now,
slant height, h
$=\sqrt{(height{)}^2+(\frac{baseedge}{2}{)}^2}$
$=\sqrt{{12}^2+9^2}$
$=\sqrt{225}$
$=15cm$

Since,
the cloth required is the lateral surface area of the pyramid.

Therefore,
the lateral surface area of the pyramid
$=4\times (\frac{1}{2}\times base\times slantheight)$

$=4\times (\frac{1}{2}\times 18\times 15)$

$=540c{m}^2$

So, $540c{m}^2$ of cloth is required to build the tent.