FINDING AREA AND PERIMTER OF REGULAR POLYGONS

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 

Area of regular polygon = 12 × Perimeter × Apothem

What is Apothem ?

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

Find the perimeter area of each regular polygon. Leave your answer in simplest form.

Example 1 :

Solution :

The given triangle must be a equilateral triangle, because it is regular polygon.

Perimeter of equilateral triangle = 3 x side 

= 3(8)

Perimeter = 24 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12 × 24× =

Example 2 :

Solution :

Number of sides = 7

Perimeter of the shape = 7 x 13.9

= 97.3

Perimeter = 97.3 cm

Length of apothem = 14.4 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12×97.3×= ×= 700.56 cm2

Example 3 :

Solution :

Number of sides = 8

Perimeter of the shape = 8 x 12

= 96 cm

Perimeter = 96 cm

Length of apothem = 14.5 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12×96×=×= 696 cm2

Example 4 :

Solution :

Number of sides = 5

Perimeter of the shape = 5 x 7.5

= 37.5 cm

Perimeter = 37.5 cm

Length of apothem = 5.1 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12×37.5×=×= 95.625 cm2

Example 5 :

Solution :

Number of sides = 9

Perimeter of the shape = 9 x 12

= 108 cm

Perimeter = 108 cm

Length of apothem = 16.5 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12×108×=×=891 cm2

Example 6 :

Solution :

Number of sides = 6

Perimeter of the shape = 6 x 10

= 60 cm

Perimeter = 60 cm

Length of apothem = 5√3 cm

Area of regular polygon = 12 × Perimeter × Apothem= 12××==1503 cm2

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