Question 1040353
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Find the area of a regular octagon inscribed in a circle with radius r. {{{highlight(cross(with_45_degree))}}}.
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This octagon is comprised of 8 isosceles triangles, each with two lateral sides of the length r and the angle of {{{360/8}}} = 45 degrees between them.

Very good.

Then the area of each of these triangles is half of the product r by itself and sin(45°)  
(see the lesson <A HREF=https://www.algebra.com/algebra/homework/Surface-area/Formulas-for-area-of-a-triangle.lesson>Formulas for area of a triangle</A> in this site).

In other words, S1 = {{{(1/2)*r^2*sin45^o)}}} = {{{(1/2)*r^2*(sqrt(2)/2)}}} = {{{(r^2*sqrt(2))/4}}}.

Now multiply it by 8, and you will get S = {{{2*sqrt(2)*r^2}}} for the area of the entire octagon.
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