To Find The Area Of A Regular Polygon

Rule. - Multiply the length of a side by half the distance from the side to the centre, and that product by the number of sides; the last product will be the area of the figure.

Example. - The side AB of a regular hexagon is 12 inches, and the distance therefrom to the centre of the figure, dc, is 10 inches; required the area of the hexagon.

- X 12 X 6 = 360 sq. in. = 2 1/2 sq. feet. Ans. 2

Pig. 6.

To Find The Area Of A Regular Polygon 106

To Find The Area Of A Regular Polygon, When The Side Only Is Given

Rule. - Multiply the square of the side by the multiplier op-posit to the name of the Polygon in the 9th column of the following Table, and the product will be the area.

Table of angles relative to the construction of Regular Polygons with the aid of the Sector, and of co-efficients to facilitate their construction without it; also, of co-efficients to aid in finding the area of the figure, the side only being given.

Names.

No.

of sides

Angle at centre.

Angle at circum.

Perpn'n.

side being 1.

Length of side rad's being 1.

Radius of circl',side being 1.

Rad.'of cir.perp being 1.

Area side being 1.

Triangle,

8

120°

60°

0.28868

1.782

.5773

2.

0.438012

Square,

4

90

90

0.5

1.414

.7071

1.414

1.

Pentagon,

5

72

108

0.6882

1.175

.8506

3.238

1.720477

Hexagon,

6

60

120

0.866

1.

1.

1.156

2.598076

Heptagon,

7

5l 3/7

128 4/7

1.0882

.8672

1.152

1.11

3.633912

Octagon,

8

45

135

1.2071

.7654

1.3065

1.08

4.828427

Nonagon,

9

40

140

1.3737

.684

1.4619

1.06

6.181824

Decagon,

10

36

144

1.5388

.618

1.618

1.05

7.694208

Undecagon,

11

32 8/11

147 3/11

1.7028

.5634

1.7747

1.04

9.36564

Dodecagon,

12

30

150

1.866

.5176

1.9318

1.037

11.196152

Note - "Angle at centre" means the angle of radii, passing from the centre to the circumference, or corners of the figure. "Angle at circumference" means the angle which any two adjoining sides make with each other.