Height of a TrapezoidDate: 02/08/2002 at 19:30:35 From: Sam Subject: Formula for the height of a trapezoid A trapezoid has parallel bases of lengths 5 and 30, and non-parallel sides of length 5 and 25. Find the height of the trapezoid. Date: 02/08/2002 at 23:45:36 From: Doctor Peterson Subject: Re: Formula for the height of a trapezoid Hi, Sam. Look at the trapezoid: D 5 C +-----+ 5 /: : \ 25 / : : \ +--+-----+--------+ A 30 B I've drawn in a rectangle that I want to cut out of the trapezoid. I'll glue the remaining triangles together; that will leave me with a triangle whose sides I know: C + 5 /: \ 25 / : \ +--+--------+ A 25 B What's interesting here is that this turns out to be an isosceles triangle. There are several ways to work out the altitude of this triangle; here's my approach: C + 5 /| \ 25 F+ |h \ / | \ \ +---+-------+ A E 25 B Draw an altitude from C to AB at E, and another from B to AC at F, dividing ABC into two congruent right triangles. Then triangle AEC is similar to triangle AFB, and altitude BF is sqrt(25^2 - 2.5^2). Then CE BF h sqrt(25^2 - 2.5^2) -- = -- so --- = ------------------ AC AB 5 25 This gives h = sqrt[(25^2 - 2.5^2)/25] = sqrt[25 - .25] = sqrt[100 - 1]/2 = 3/2 sqrt(11) - Doctor Peterson, The Math Forum http://mathforum.org/dr.math/ |
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