# Area of an Octagon Formula

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An octagon is a polygon which has a total of 8 sides. An octagon is a closed geometric shape and area of an

octagon is the region covered inside by the bounded sides of the octagon. A regular octagon is the octagon

with all the side lengths equal to each other. Area of a regular octagon is the half times the product of its

perimeter and its apothem.

Example 1: Calculate the area of the octagon the side length is 8m.

Apothem of regular polygon is the line drawn from the center of the polygon to the midpoint of any of the

sides.

Apothem = (Side length)/ (2 * tan(180°/n))where n = number of sides

Apothem = 8m/ (2 * tan(22.5°) = 9.66m

Area of a regular polygon, A = 1/2 * Perimeter * apothem

For a regular octagon there are ‘8’ sides.

Hence Perimeter = n * side length= 8 * 8= 64m

Hence the area of the regular octagon, A = 1/2 * (64m) * (9.66m) = 309m2

Example 2: Calculate the area of the octagon the side length is 10m.

Apothem of regular polygon is the line drawn from the center of the polygon to the midpoint of any of the

sides.

Apothem = (Side length)/ (2 * tan(180°/n))where n = number of sides

Apothem = 10m/ (2 * tan(22.5°) = 12.07m

Area of a regular polygon, A = 1/2 * Perimeter * apothem

For a regular octagon there are ‘8’ sides.

Hence Perimeter = n * side length= 8 * 10= 80m

Hence the area of the regular octagon, A = 1/2 * (80m) * (12.07m) = 482.8m2