Calculating Octagon Area from Perimeter of 72

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SUMMARY

The area of a regular octagon with a perimeter of 72 inches, where each side measures 9 inches, can be calculated by dividing the shape into triangles. The method involves recognizing the octagon as a square with missing corners, specifically 45-45-90 triangles. By determining the height using the tangent function and calculating the area of one triangle, the total area is found by multiplying by 8. The calculated area is approximately 390.96 square inches.

PREREQUISITES
  • Understanding of geometric shapes, specifically regular octagons
  • Knowledge of trigonometric functions, particularly tangent
  • Ability to calculate the area of triangles
  • Familiarity with basic algebra for manipulating equations
NEXT STEPS
  • Study the formula for the area of a regular octagon
  • Learn about 45-45-90 triangles and their properties
  • Explore trigonometric functions and their applications in geometry
  • Practice calculating areas of various polygons using decomposition methods
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Students studying geometry, mathematics educators, and anyone interested in understanding polygon area calculations.

Dagenais
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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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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.
 
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.
 

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