# AREA OF REGULAR POLYGON GIVEN SIDE LENGTH

What is polygon ?

polygon can be defined as a flat or plane, two-dimensional closed shape with straight sides. It does not have curved sides.

Regular polygon :

A polygon having equal sides and equal angles is a regular polygon.

To find area of regular polygon, we use the formula

What is Apothem ?

A line from the center of a regular polygon at right angles to any of its sides.

Find the area of each of regular polygon.

Problem 1 :

Solution :

Number of sides of the given polygon = 6

∠AOB = 360/6 ==> 60

∠COB = 60/2 ==> 30

Apothem = OC

tan θ = BC/OC

tan 30 = 9/OC

0.577 = 9/OC

OC = 9/0.577

OC = 15.59 (Apothem)

Perimeter of the polygon = 618) ==> 108 ft

Area of polygon = (1/2) x Perimeter x apothem

Area of polygon = (1/2) x 108 x 15.59

= 841.86 ft2

Problem 2 :

Solution :

Number of sides of the given polygon = 3

∠AOB = 360/3 ==> 120

∠COB = 120/2 ==> 60

In triangle OCB :

Apothem = OC

tan θ = BC/OC

tan 60 = 4/OC

1.732 = 4/OC

OC = 4/1.732

OC = 2.309

OC = 2.309 (Apothem)

Perimeter of the polygon = 3(4) ==> 12 inches

Area of polygon = (1/2) x Perimeter x apothem

Area of polygon = (1/2) x 12 x 2.309

= 13.854 square inches

Problem 3 :

Solution :

Number of sides of the given polygon = 6

∠AOB = 360/6 ==> 60

∠COB = 60/2 ==> 30

In triangle OCB :

Apothem = OC

tan θ = BC/OC

tan 30 = 6/OC

0.577 = 6/OC

OC = 6/0.577

OC = 10.39

OC = 10.39 (Apothem)

Perimeter of the polygon = 6(12) ==> 72 inches

Area of polygon = (1/2) x Perimeter x apothem

Area of polygon = (1/2) x 72 x 10.39

= 374.04 square meter

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