數學知識交流---幾何(2)

Let the trapezium be ABCD with AD//BC. A line passing through D and parallel to AB is drawn to cut BC at M, that is DM = AB.
(1) For triangle DMC, DM = AB (given), DC (given) and MC = BC - AD, that means length of the 3 sides are known, then by Heron's formula, area of triangle DMC can be found.
(2) Height of triangle DMC x MC/2 = Area of triangle DMC, so height of triangle = height of trapezium can be found.
(3) ABMD is a parallelogram, area = height x BM, so can also be found.
In summary, if 4 sides of a trapezium is given, its area can be found.

2011-06-20 21:04:53 補充：
Note : Length of BM = AD.

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