The eight sided geometric figureCalled an octagon or octagon, it is usually represented in two dimensions as a drawing or a flat object, a common example being a traffic sign. The area of an octagonal figure it is easily calculated with basic mathematics. Calculating the side, sides, or perimeter of an octagon is a simple matter of adding the lengths of the sides. Although rare, three-dimensional objects can also be formed with eight sides and the lateral area is calculated with the same formula as a square or rectangle. At OneHowTo we want to make it easy for you and explain how to calculate the perimeter and area of an octagon.
Steps to follow:
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The first thing you have to do is measure the length of each side of the octagon; It should be noted that this polygon can be regular, that is, all its sides are identical and measure the same, or irregular if the sides are different.
2
To know the perimeter of a regular octagon -like the one you see in the drawing below-, you must multiply the length of one side of the octagon by the number of sides which in the octagon is 8. So the mathematical formula says that P = l · 8
For example, if all eight sides of the octagon have an identical length of five centimeters, the perimeter of the octagon is calculated:
5cm x 8 sides = 40cm perimeter
3
For irregular octagons, you will need to determine the perimeter by calculating each side separately and the sum of these figures.
For example: if the first side is 5 centimeters, the second side is 4 centimeters, the third side is 7 centimeters, the fourth is 3 centimeters, and sides five, six, seven and eight are 10 centimeters, the perimeter of the octagon would be equal to 60 centimeters
Perimeter = 5 + 4 + 7 + 3 + 10 + 10 + 10 + 10 = 60 cm.
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If what we want is calculate the surface or area of a regular octagon, we must apply the mathematical formula that says that the area is equal to the multiplication of the perimeter by the apothem divided by two.
So, we already know how to calculate the perimeter of an octagon, but what is the apothem? This is the distance that separates the center of the polygon from the center point of each side of the octagon; If you look at the image, we have marked it in green.
Continuing with the example, if each side is 5 cm and the apothem is 10 cm, we calculate the surface of the octagon by multiplying the side by 8 and by the apothem and dividing the result by two:
S = (5 cm · 8 cm) · 10/2 = 40 · 10/2 = 200 cm²
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Another option just as valid for calculate the area of a regular octagon is to divide the polygon into eight equal triangles, find their area, and then multiply it by eight. In this way, the apothem of the regular octagon will be equal to the height of each of these triangles and the side equal to the base, which are the two elements we need to calculate the area of a triangle.
Thus, the surface of a triangle is obtained by applying the formula that says that it is equal to the multiplication of the base times the height and dividing its result by two:
S = (5 · 10) / 2 = 50/2 = 25 cm²
Once this is done, we will only need multiply the surface or area of the triangle by 8, which is the number of regular triangles that make up the eight-sided polygon:
S = 25 · 8 = = 200 cm²
As we can see, the result is the same despite applying two different methods.
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Advice
- Remember that whenever you calculate distances, surfaces, angles, etc., you must say the units in the result.