SOLUTION: The octagon has a radius of 10. Find area.

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Question 957218: The octagon has a radius of 10. Find area.
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!


The central angle is %22360%B0%22%2F8+=+%2245%B0%22

The SAS formula for the area of a triangle is

"The area of a triangle is equal to one-half the product of
two sides multipled by the sine of the included angle.

Area of the triangle = expr%281%2F2%29%2810%29%2810%29sin%28%2245%B0%22%29%22%22=%22%22%2850%29sqrt%282%29%2F2%22%22=%22%2225sqrt%282%29

and as we see below:



the regular octagon is composed of 8 such triangles,
all congruent.  Therefore:

The area of the regular octagon = 8%2A25sqrt%282%29%22%22=%22%22200sqrt%282%29.

That's approximately 282.8427125 square units.

Edwin