Geometry

A square with sides of is inscribed in a circle. What is the area of one of the sectors formed by the radii to the vertices of the square?

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  1. let the radius be r
    then the area of one of the sectors would simply be 1/4 of the area of the circle,
    which would be (1/4)πr^2 or πr^2/4

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  2. if the sides are each 6 of the square then how would you find the segment?

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  3. The 6 is the hypotenuse of a right-angled triangle with the other sides as the radius
    r^2 + r^2 = 36
    r^2 = 18
    r = √18

    sector = (1/4)π(√18)^2 = 9π/2

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