# The Sum of Length, Breadth and Height of a Cuboid is 38 Cm and the Length of Its Diagonal is 22 Cm. Find the Total Surface Area of the Cuboid. - Geometry

The sum of length, breadth and height of a cuboid is 38 cm and the length of its diagonal is 22 cm. Find the total surface area of the cuboid.

#### Solution

Let length, breadth and height of the cuboid be l cm, b cm and h cm, respectively.

Given: l + b + h = 38 cm and diagonal = 22 cm.

To find: total surface area of the cuboid

Diagonal of cuboid = sqrt(l^2+b^2+h^2)

sqrt(l^2+b^2+h^2)=22

l^2+b^2+h^2=484" .........(i)"

"As "l+b+h=38

(l+b+h)^2=1444

l^2+b^2+h^2+2(lb+bh+lh)=1444

484=2(lb+bh+lh)=1444" .................From(i)"

2(lb+bh+lh)=960

The surface area of the cuboid is 960 cm2.

Concept: Surface Area of a Combination of Solids
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