Question

a cuboid has total surface area of 60m square and lateral surface area of 40 m square . find area of its base

Answer 1

TSA = 60 m^2

=> 2(lb+bh+hl) = 60

=> 2lb + 2bh + 2hl = 60 -------(1)

LSA = 40 m^2

=> 2(lh +bh) = 40

=> 2hl + 2bh = 40 -----------(2)


On subtracting equation 2 from 1, we get

2 lb= 20

=> l *b = 10

Area of Base = 10 m^2

Answer 2

Given:

The total surface area of the cuboid = 60m

The lateral surface area of the cuboid = 40 m

To Find:

Area of base of cuboid

Solution:

As we know,

Total Surface Area of cuboid =  2(lb+bh+hl)

Where l = length

          b = breadth

          h = height

⇒  60 = 2(lb+bh+hl)

⇒ 30 = lb + bh + hl  -------(i)

As we know,

Lateral Surface Area of cuboid  =  2(lh +bh)

⇒ 40 = 2(lh +bh)

⇒ 20 = hl + bh  -----------(ii)

subtract equation (ii) from (i),

so,

⇒ ( lb + bh + lh) - (lh + bh) = (30-20)

⇒ lb= 10

⇒( l×b) = 10

⇒ ( length×breadth) = 10

The area of the base of the cuboid is given by,

= (length×breadth)

= 10

Hence, the area of the Base of the cuboid is 10 m².