The image above is a Trapezium

To compute the area of a trapezium, three essential parameter is needed and they are the length of the top side (a), length of the bottom side (b) and the height of the trapezium (h).

The formula for calculating the area of a trapezium is;

**A** = 0.5[a + b]h

Where;

A = Area of a trapezium

a = length of the top side of the trapezium

b = length of the bottom side of the trapezium

h = height of the trapezium

Let’s solve an example;

Find the area of a trapezium where length of top side (a) is 7 cm, length of bottom side (b) is 12 cm and height of trapezium (h) is 10 cm.

This implies that;

a = Length of top side of the trapezium = 7 cm

b = Length of bottom side of the trapezium = 12 cm

h = Height of the trapezium = 10 cm

**A** = 0.5[a + b]h

**A** = 0.5[7 + 12]10

**A** = 0.5[19]10

**A** = 95

Therefore, the **area of a trapezium** is **95 cm ^{2}**

**How to Calculate the Height of a Trapezium when the Area, Length of top side and Length of bottom side of the Trapezium is given.**

The formula is h = ^{A} / _{0.5(a + b)}

Where;

A = Area of the trapezium

a = Length of the top side of the trapezium

b = Length of the bottom side of the trapezium

Let’s solve for an example;

Given that the length of top side (a) is 10 cm, length of bottom side (b) is 14 cm and the area of the trapezium is 20 cm^{2} Find the height of the trapezium?

This implies that;

A = Area of the trapezium = 20 cm^{2}

a = Length of top side of the trapezium = 10 cm

b = Length of bottom side of the trapezium = 14 cm

h = ^{A} / _{0.5(a + b)}

h = ^{20} / _{0.5(10 + 14)}

h = ^{20} / _{0.5(24)}

h = ^{20} / _{12}

h = 1.667

Therefore, the **height of the trapezium** is **1.667 cm.**