Question

A cuboidal has total surface area of $372c{m}^2$ and its lateral surface area is $180c{m}^2$, find the area of its base.

Answer 1

Total surface area of cuboid $=372c{m}^2$
Lateral surface area $=180c{m}^2$
Let length of cuboid $=l$
Breadth of cuboid $=b$
Height of cuboid $=h$

Now, total surface area of cuboid $=372c{m}^2$
$\Rightarrow 2(lb+bh+hl)=372$
$\Rightarrow (lb+bh+hl)=186....\left(1\right)$

Lateral surface area of cuboid $=189c{m}^2$
$\Rightarrow 2(l+b)h=180$
$\Rightarrow (l+b)h=90$
$\Rightarrow lh+bh=90$ ... (2)

Using equation (1) and (2), we get
$lb+90=186$
$lb=96$
$\Rightarrow$ Area of base of cuboid $=96c{m}^2$

Hence, the required area is $96c{m}^2$