# geometry

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An isosceles trapezoid with that bases 16 in and 34 in are inscribed in a circle such that one of the bases is the diameter. Find the area of the trapezoid.

• geometry -

OK 34 inches is the diameter of the circumscribed circle. The radius of the circle is 17 inches. The distance of the other two corners from the center of the circle is also 17 inches.

It would help to draw a figure. A perpendicular to the diameter bisecting the smaller parallel side will divide it into two sections 8 inches long. A line from the diameter to the parallel side will have length sqrt[(17)^2 - (8)^2] = 15 inches. That is the height of the trapezoid.

The area is (1/2)(8 + 17)*15 = 187.5 in^2.

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