Area of Polygon Examples

Example 1: Find the area of the given polygon.

Solution:

We are given the above figure which is a Hexagon and we are supposed to find out the area of the above figure MNOPQR.

Area of the figure MNOPQR = Area of triangle MNO + Area of triangle PQR + Area of rectangle MOPR

Area of the figure MNOPQR = (1/2) × MO × NK +(1/2) × PR × QL + PO × MO

Area of the figure MNOPQR = (1/2) × 20 × 5 + (1/2) x 20 × 5 + 13 × 20

Area of the figure MNOPQR = 10 × 5 + 10 × 5 + 260

Area of the figure MNOPQR = 50 cm²+ 50 cm² + 260 cm²

Area of the figure MNOPQR = 360 cm²

Hence, the area of the given Hexagon MNOPQR is 360 cm².

Example 2: Find the area of the given polygon.

Solution: 

We are given the above figure which is a Hexagon and we are supposed to find out the area of the above figure ABCDEF.

Area of the figure ABCDEF = Area of Trapezium DEFC + Area of Square ABCF

Area of the figure ABCDEF = (1/2) × (ED+FC) × EK + (AF)²

Area of the figure ABCDEF = (1/2) × (7 + 18) × 8 + (18)²

Area of the figure ABCDEF = 4 × 25 + 18 × 18

Area of the figure ABCDEF = 100 cm² + 324 cm²

Area of the figure ABCDEF = 424 cm²

Hence, the area of the given Hexagon ABCDEF is 424 cm²

Example 3: Find the area of the given polygon.

Solution: 

We are given the above figure which is a Pentagon and we are supposed to find out the area of the above figure ABCDE.

Area of the figure ABCDE = Area of triangle AHE + Area of Trapezium DEHF + Area of triangle DFC + Area of Triangle ABC

Area of the figure ABCDE = (1/2) × AH × HE + (1/2) × (EH+DF) × HF + (1/2)× FC × DF + (1/2) × AC × GB

Area of the figure ABCDE = (1/2) × 50 × 30 + (1/2) × (30+20) × 70 + (1/2) × 30 × 20 + (1/2) × 150 × 50

Area of the figure ABCDE = 25 × 30 + 50 × 35 + 15 × 20 + 150 × 25

Area of the figure ABCDE = 750 m² + 1750 m²+ 300 m²+ 3750 m²

Area of the figure ABCDE = 6550 m²

Hence, the area of the given Pentagon ABCDE is 6550 m².

Example 4: Find the area of the given polygon, where the length of the diagonal AC is 18 cm.

Solution: 

We are given the above figure which is a quadrilateral, and we are supposed to find out the area of the above figure ABCD.

Area of the quadrilateral ABCD = Area of triangle ABC + Area of triangle ADC

Area of the quadrilateral ABCD = (1/2) × AC × DM + (1/2) × AC × BN

Area of the quadrilateral ABCD = (1/2) × AC × (BN+DM)

Area of the quadrilateral ABCD = (1/2) × 18 × (6+5)

Area of the quadrilateral ABCD = 9 × 11 cm²

Area of the quadrilateral ABCD = 99 cm²

Hence, the area of the given quadrilateral is 99 cm².

Example 5: Find the area of the given polygon.

Solution: 

We are given the above figure which is a Pentagon and we are supposed to find out the area of the above figure ABCDE.

Area of the figure ABCDE = Area of triangle AGB + Area of Rectangle BCHG + Area of triangle AFE + Area of Trapezium DEFH

Area of the figure ABCDE = (1/2) × AG × BG + BG × GH + (1/2) × AF × FE + (1/2) × (DH+EF) × FH

Area of the figure ABCDE = (1/2) × 8 × 4 + 4 × 3 + (1/2) × 5 × 5 + (1/2) × (3+5) × 6

Area of the figure ABCDE = 4 × 4 + 4 × 3 + 2.5 × 5 + 3 × 8 cm²

Area of the figure ABCDE = 16 + 12 + 12.5 + 24 cm²

Area of the figure ABCDE = 64.5 cm²

Hence, the area of the given Pentagon ABCDE is 64.5 cm².

Example 6: Find the area of the given polygon.

Solution: 

We are given the above figure which is a Pentagon, and we are supposed to find out the area of the above figure ABCDE.

Area of the figure ABCDE = Area of triangle ADE + Area of triangle CHD + Area of Trapezium BCHF + Area of triangle ABF

Area of the figure ABCDE = (1/2) *AD*GE + (1/2) *HD*CH + (1/2) *(CH+BF)*FH + (1/2) *AF*BF

Area of the figure ABCDE = (1/2) × 7 × 4 + (1/2) × 1 × 4 + (1/2) × (4+3) × 4 + (1/2) × 2 × 3 cm²

Area of the figure ABCDE = 2 × 7 + 2 + 7 × 2 + 1 × 3 cm²

Area of the figure ABCDE = 14 + 2 + 14 + 3 cm²

Area of the figure ABCDE = 33 cm²

Hence, the area of the given Pentagon ABCDE is 33 cm².

Area of the Polygon is the area enclosed by the boundary of the polygon. A polygon is a closed, two-dimensional shape with straight sides. Each side of a polygon is a line segment, and the points where the sides meet are called vertices.

A polygon is a figure formed by joining ‘n’ straight lines such that it forms a closed figure. It has n-sides and there are different types of polygon, such as triangle, square, pentagon, etc. The area of the polygon is found by various methods and different types of polygons have different formulas to calculate its area. For example, suppose we have to find the area of a square (4-sided polygon) then its area is found by the formula, (side)². Similarly, the area of other polygons is found.

Let’s learn more about Area of Polygons with formula, derivation and examples in detail below.