## How to Calculate and Solve for the Area, Length, Width and Height of a Cuboid | Nickzom Calculator

The image above represents a cuboid.
To compute the area of a cuboid requires three essential parameters which are the length, width and height of the cuboid.

The formula for computing the area of a cuboid is:

A = 2(lw + lh + wh)

Where:
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example
Find the area of a cuboid with a length of 5 cm, width of 3 cm and a height of 9 cm.

This implies that:
l = length of the cuboid = 5
w = width of the cuboid = 3
h= = height of the cuboid = 9

A = 2(lw + lh + wh)
A = 2(5 x 3 + 5 x 9 + 3 x 9)
A = 2(87)
A = 174

Therefore, the area of the cuboid is 174 cm2.

Calculating the Length of a cuboid when Area, Width and Height are Given

The formula is l = A – 2(w)(h) / 2(w) + 2(h)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the length of a cuboid with an area of 140 cm2 , a width of 4 cm and a height of 12 cm

This implies that;
A = Area of the cuboid = 140 cm2
w = width of the cuboid = 4 cm
h  = height of the cuboid = 12 cm

l =  A – 2(w)(h) / 2(w) + 2(h)
l = 140 – 2(4)(12) / 2(4) + 2(12)
l = 140 – 96 / 8 + 24
l = 44 / 32
l = 1.375 cm

Therefore, the length of the cuboid is 1.375 cm.

Calculating the Width of a cuboid when Area, Length and Height are Given

The formula is w = A – 2(l)(h) / 2(l) + 2(h)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the width of a cuboid with an area of 200 cm2 , a length of 5 cm and a height of 12 cm

This implies that;
A = Area of the cuboid = 200 cm2
l = length of the cuboid = 5 cm
h  = height of the cuboid = 12 cm

w =  A – 2(l)(h) / 2(l) + 2(h)
w = 200 – 2(5)(12) / 2(5) + 2(12)
w = 200 – 120 / 10 + 24
w = 80 / 34
w = 2.353 cm

Therefore, the width of the cuboid is 2.353 cm.

Calculating the Height of a cuboid when Area, Length and Width are Given

The formula is h = A – 2(l)(w) / 2(l) + 2(w)

Where;
A = Area of the Cuboid
l = Length of the Cuboid
w = Width of the Cuboid
h = Height of the Cuboid

Let’s solve an example:
Find the height of a cuboid with an area of 300 cm2 , a length of 6 cm and a width of 2 cm

This implies that;
A = Area of the cuboid = 300 cm2
l = length of the cuboid = 6 cm
w  = width of the cuboid = 2 cm

h =  A – 2(l)(w) / 2(l) + 2(w)
h = 300 – 2(6)(2) / 2(6) + 2(2)
h = 300 – 24 / 12 + 4
h = 276 / 16
h = 17.25 cm

Therefore, the height of the cuboid is 17.25 cm.