Math CentralQuandaries & Queries


Question from Abby, a student:

An isosceles trapezoid whose bases have lengths 12 and 16 is inscribed in a circle of radius 10. The center of the circle lies in the interior of the trapezoid. Find the area of the trapezoid

Hi Abby,

In my diagram C is the center of the circle and B is the midpoint of the side of the trapezoid of length 12.


Triangle ABC is a right triangle (why?), the length of CA is 10 and the length of AB is 6. Use Pythagoras theorem to find the length of BC. Use a similar argument to find the length of CD.

Now you know the lengths of the parallel sides of a trapezoid and the distance between the parallel sides. What is its area?


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