Trapezoid and Circle

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In the figure above, EF is a diameter of the circle with center O and is tangent at each end to the trapezoid ABCD. If the area of the circle is , the length of AD is 20 and the length of BC is 10, what is the area of the ABCD?

Review: Trapezoid and Circle


Explanation

This diagram is a little strange, but we want the area of the trapezoid and we are given all the pieces to find it. Both bases of the trapezoid are given to us directly, and the height can be inferred from the area of the circle. Using the circle area formula:



So . That means that the height of the trapezoid will be the diameter, which is 30. The area of a trapezoid is the height times the average of the bases (you can think of averaging the bases as computing the base of an equivalent rectangle), so



The correct answer is (C).


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