Question

a cuboid has total surface area of 50 m square and Lateral surface area is 30 m square find the area of its base

Answer 1

tsa = total surface area
lsa = lateral surface area
tsa - lsa = 50-30 = 20
2(lb+bh+hl) - 2(bh+hl) = 20
2lb = 20
lb = 10 m2
so area of base = 10 m2

Answer 2

Answer:

The area of the base of the cuboid is  $10 m^{2}$

Solution:

The formula for the total surface area of cuboid is  

$T.S.A of cuboid=2(lb+bh+lh)$

Total surface area = 50 m^{2}

So, $2(lb +bh +lh) = 50$ …………….. (i)

The formula for the lateral surface area of cuboid is  

$L.S.A of cuboid=2(bh+lh)$

Lateral surface area = $30 m^{2}$

So, $2(bh+hl) =30$ ………………. (ii)

Now subtracting (i) and (ii),

$2(lb +bh +lh) - 2(bh+hl) =50-30$

$2lb + 2bh +2lh -2bh – 2hl = 20$

$2lb = 20$

$lb = 10$

So the area of the base is $10 m^{2}$