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 cm**^{2}.

**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 cm^{2} , a width of 4 cm and a height of 12 cm

This implies that;

A = Area of the cuboid = 140 cm^{2}

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 cm^{2} , a length of 5 cm and a height of 12 cm

This implies that;

A = Area of the cuboid = 200 cm^{2}

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 cm^{2} , a length of 6 cm and a width of 2 cm

This implies that;

A = Area of the cuboid = 300 cm^{2}

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.**

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