Area Of Polygon

You are already acquainted with the term area. It is defined as the region occupied inside the boundary of a flat object or figure. The measurement is done in square units with the standard unit being square meters (m2). For the computation of area, there are pre-defined formulas for Squares, Rectangles, Circle, Triangles, Trapeziums, etc. However, for an irregular polygon, the area is calculated by viewing it as a combination of 2 or more regular polygons. In this article, you will learn about the area of a polygon in general.

Area of Polygon

For finding the area of a polygon which is not regular or its formula is not defined, we split the figure into triangles, squares, trapezium, etc. The purpose is to visualize the given geometry as a combination of geometries for which we know how to calculate the area. We then calculate the area for each of the part and then add them up to obtain the area of the polygon.

For example, consider the polygon shown below:

Area Of Polygon

This polygon can be divided into a combination of triangles and trapezium.

Area Of PolygonArea Of Polygon

We can calculate the area considering any of the above divisions. In the first figure, we can sum up the area of the triangle as well as the trapezium to obtain the area of polygon. In the second one, we add the areas of the three triangles to get the area of polygon. In either case, the result is same.

Example: Find the area of polygon ABCDEFG. The measurements (in cm) are shown in the figure.

Area of Polygon

Solution: The polygon can be split into two trapeziums and a triangle.

Area of Polygon

So, the area of polygon ABCDEFG is given by the sum of the area of trapezium ABCG and CDFG and the area of triangle DEF.

Height of trapezium ABCG = 3 cm

Height of trapezium CDFG = (6 – 3) = 3 cm

Height of triangle DEF = (8 – 6) = 2 cm

Area of trapezium ABCG = (sum of parallel sides) × height/2 = (4 + 7)×3/2 = 33/2 = 16.5 cm2

Area of trapezium CDFG = (7 + 4) ×3/2 = 33/2 = 16.5 cm2

Area of triangle DEF = (base ×height)/2 = (4 × 2)/2 = 8/2 = 4 cm2

So, area of polygon ABCDEFG = area of ABCG + area of CDFG + area of DEF

= 16.5 + 16.5 + 4 = 37 cm2

Practise This Question

PQRS is a quadrilateral in which PQ=52cm, QR=52cm, RS=8cm, SP=6cm, PSR=PQR=90. Then its area is