SOLUTION: A regular octagon has an apothem of 9cm. Find its exact area.
I have tried numerous times to work out this problem, but I got confused.
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-> SOLUTION: A regular octagon has an apothem of 9cm. Find its exact area.
I have tried numerous times to work out this problem, but I got confused.
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Question 871265: A regular octagon has an apothem of 9cm. Find its exact area.
I have tried numerous times to work out this problem, but I got confused.
You can put this solution on YOUR website! The polygon is made up of 8 triangles. We need to find the area of one of the triangles and multiply by 8. The apothem is the radius of the incircle which is also equal to the height of the triangle. The angle opposite the base of the triangle will be equal to 360/8 = 2*pi/8 since there are 8 triangles altogether. The right triangle formed by half the base with the height equal to the apothem will have half this value (=pi/8). The tangent of this inside angle will be equal to b/9 (b=base, 9=length of apothem) -> b = 9*tan(pi/8)
So the area of one of the triangles = b*9 = 81*tan(pi/8).
Since there are 8 triangles, the area of the whole octagon is equal to 8*81*tan(pi/8) = 648*tan(pi/8)
Using the half-angle formula for tan(pi/8), we can write the answer as
