Calculating Octagon Area from Perimeter of 72

In summary, to solve for the area of an octagon with a total perimeter of 72 inches, you can break it up into triangles and use the known side length of 9 inches to find the missing corners. By dividing one of the triangles into two 90-degree triangles and using the tangent ratio, you can find the height and then calculate the area of one triangle. Multiply that by 8 to get the total area of the octagon, which is approximately 390.96 inches squared.
  • #1
Dagenais
290
4
I forgot the equation on how to solve for the area of an octagon. No information is given except that the total perimeter is 72 inches since we know that each side is 9-inch long.

I looked up some stuff on the internet but it said we had to know the area from the middle of the shape to the outer edge (radius) in which I don't.

Edit: Not sure, but I think the answer is somewhere around 390.96 inches squared?
 
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  • #2
You can break it up into triangles. If all of the interior angles and all sides are congruent, then you can think of it as a square with missing corners. The missing corners are 45-45-90 triangles.
 
  • #3
I separated the Octagon into triangled. Then, I chose a triangle and cut it in half turning it into a 90 degree triangle (I have the measurement of 2 of the angles now).

I knew what the base was (half of 9), then I used Tan to find the side of the height.

After I did that, I found the area of the triangle and multiplied it by 8.
 

What is an octagon and how is it different from other shapes?

An octagon is a polygon with 8 sides and 8 angles. It is different from other shapes because it has a specific number of sides and angles, unlike circles or triangles which can have varying numbers of sides.

What is the formula for calculating the area of an octagon?

The formula for calculating the area of an octagon is: Area = 2(1+√2) x (perimeter/2)^2, where the perimeter is the total length of all 8 sides of the octagon.

How do I find the perimeter of an octagon with a perimeter of 72?

The perimeter of an octagon is equal to the sum of all the sides. Since we know the perimeter is 72, we can divide it by 8 to get the length of one side. Then, multiply that by 8 to get the total perimeter.

What units should I use for the perimeter and area of an octagon?

The units used for the perimeter and area of an octagon should be consistent. If the perimeter is measured in feet, then the area should be measured in square feet. If the perimeter is in meters, then the area should be in square meters.

Can I use the same formula to calculate the area of any octagon?

Yes, the formula for calculating the area of an octagon can be used for any regular or irregular octagon, as long as you know the perimeter. However, for irregular octagons, it may be easier to divide the octagon into smaller shapes (such as triangles) and calculate the area of each shape separately.

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