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ABCD is a quadrilateral with AD = BC, AB = 40, CD = 20, and angle DAB + angle ABC = 90 deg. If the area of the quadrilateral is N, find N/100.

1. 6
2. 8
3. 4
4. 5

Correct answer: 6

Solution

Because angle DAB + angle ABC = 90 deg, extending sides AD and BC meets at a right angle. With AD = BC, the configuration forms a right triangle on AB minus a similar right triangle on CD. Using AB = 40 and CD = 20 (a 2:1 ratio of parallel-like segments) the area works out to 600, so N/100 = 6.

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