A trapezium is a quadrilateral that has only one pair of parallel sides.

Consider the area of the following trapezium.

To calculate the area of a trapezium, divide it into a rectangle and two triangles as shown below.

Join the triangular ends so that the trapezium is divided into a triangle and rectangle separately. The base of the triangle is the difference between the lengths of two parallel sides. That is, a – b.

Demonstration:

Find the area of the following trapezium.

Solution:

a = 30 cm , b = 20 cm, h = 16 cm

A = ½ (a+b)h

= ½ (30+20) 16

= ½ (50)16

= 400

So, the area of the trapezium is 400cm^{2}.

Area of any Regular Polygon

A regular polygon is a polygon where all the sides are the same length and all the angles are equal.

How to find the area of a regular polygon?

The apothem of a regular polygon is a line segment from the center of the polygon to the midpoint of one of its sides. The area of any regular polygon is equal to half of the product of the perimeter and the apothem.

Area of regular polygon = where p is the perimeter and a is the apothem