Area of A Octagon Formula

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Anoctagon is a geometric figure which belongs to the polygon group of geometric shapes. If a polygon has ‘8’ sides, then that polygon is called anoctagon. A regular octagon is the octagon whose length of the sides are equal to each other. Area of anoctagon is the area covered inside the shape by its sides and can be calculated using its side lengths.


Example 1: Calculate the area of the regular octagon if the side length is 4m.

Since it’s a regular octagon, all the sides are equal to = 4m
Like shown above in the diagram, the sides of the octagon can be extended such that it forms a square.
According to Pythagorean theorem, x2 + x2 = 42; 2x2 = 16
x = √8m
Total side length for the square= 4 + √8 + √8 = 9.657m
Area of square= (9.657m) 2 = 93.25m2
Area of 4 triangles= 4 (1/2 * √8 * √8) = 16.0m
Area of octagon, A = Area of square – Area of 4 triangles = 93.25 – 16.0 = 77.25m2


 
Example 2: Calculate the area of the regular octagon if the side length is 6m.

Like shown in the above example, according to Pythagorean Theorem, x2 + x2 = 62

2x2= 36; x= 3√2m

Total side length for the square= 4+ 3√2+ 3√2 = 4 + 6√2m

Area of square= (4+ 6√2m) 2 = 156.25m2

Area of 4 triangles= 4 (1/2* 3√2* 3√2) = 36.0m

Area of octagon, A = Area of square – Area of 4 triangles = 156.25 – 36.0

A = 120m2(approx.)


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