Draw line BH vertically intersect CD at point H. Since height h is 4, which means the length of BH = 4. And by the graph above, we can get angle BCD is 60°, angle HBC is 30°. Therefore, length CH is half of BC. On the basis of Using Pythagorean theorem we deduce that length BC = 8/(V3) and length CH = 4/(V3)
The trapezoid area formula is (AB + CD) * BH / 2.
By (1) alone, length AB is available, height BH is available as well, but not length CD. Thus,
(1) alone is NOT sufficient.
By (2) alone, we can deduce that it's a isosceles trapezoid since angle ADC = BCH = 60°, but have no idea of AB.
Finally, with (1) and (2) together, AB = 5, CD = 2*(CH)+AB = 8/(V3)+5, BH = 4, the area is
(5+5+8/(v3))*4/2 = 20+16/(V3). These 2 conditions together do make sense.
(!!!! Note that V means square root. V3 = square root of 3. !!!!)
Pls find details in attachment.
Hope it helps.
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Attachments
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- DS.trapezoid.doc
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