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How do you algebraically determine the perimeterof arectangular octagon inscribed in a circle of diameter 15cmEach side of the octagon is 6.9cm from the centre of the circle?
Wiki User
∙ 15y ago
We know that an octagon is an eight-side polygon. Since each side has the same distance form the center of the circumscribed circle of the octagon, this octagon is a regular octagon. If we draw the radii of the circle (their endpoints there are at the vertexes of the octagon), we form 8 isosceles triangle, which radius represents two their congruent sides with a measure of 7.5 cm, and the distance drawn from the center of the circle to the sides of the octagon represents their altitudes with a measure of 6.9 cm. So, by using the Pythagorean theorem we can find the half of the side of the octagon, which is:
7.5)^2 - (6.9)^2 = 8.64
Since one half of the octagon side is square root of 8.64, the whole side is 2(square root of 8.64)
Thus the perimeter of this octagon is approximately 47 cm [8 x 2(square root of 8.64)].
Wiki User
∙ 15y ago
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