A regular octagon is inscribed in a circle with r = 8 inches
- Thread starter NEHA
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Since you are asking how to go about figuring this, I will assume that you haven't been given the general formula, and need to work it out yourself.
You've drawn the octagon and the circle, and you've drawn the radius lines from the center to the vertices where the octagon touches the circle, right? So you've got a circle divided into sectors, with a triangle inside each sector.
Pick one of the sectors. Draw a line from the center to the midpoint of the other side of the triangle. This is the altitude line, and splits the triangle into two right triangles. Pick one of the right triangles.
You know the length of the hypotenuse. What is the length of the altitude? What is the length of the base? Use these to find the area of the right triangle. Multiply to get the area of the entire octagon.
If you get stuck, please reply showing how far you have gotten. Thank you.
Eliz.
You've drawn the octagon and the circle, and you've drawn the radius lines from the center to the vertices where the octagon touches the circle, right? So you've got a circle divided into sectors, with a triangle inside each sector.
Pick one of the sectors. Draw a line from the center to the midpoint of the other side of the triangle. This is the altitude line, and splits the triangle into two right triangles. Pick one of the right triangles.
You know the length of the hypotenuse. What is the length of the altitude? What is the length of the base? Use these to find the area of the right triangle. Multiply to get the area of the entire octagon.
If you get stuck, please reply showing how far you have gotten. Thank you.
Eliz.