Area Of A Trapezium

 

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

Consider the area of the following trapezium.

http://www.mathsteacher.com.au/year8/ch12_area/04_trap/Image15458.gif

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

http://www.mathsteacher.com.au/year8/ch12_area/04_trap/Image15459.gif

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.

http://www.mathsteacher.com.au/year8/ch12_area/04_trap/Image15460.gif
http://www.mathsteacher.com.au/year8/ch12_area/04_trap/Image15461.gif

Demonstration:

Find the area of the following trapezium.

http://www.mathsteacher.com.au/year8/ch12_area/04_trap/Image15462.gif

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 400cm2.

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.

area of polygon with apothem

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 = https://www.onlinemathlearning.com/image-files/clgeo20.gif where p is the perimeter and a is the apothem