What's the fastest way to do these math problems?

gcf101
Sat, 18 Jul 2009 01:48:08 +0000

Cutting into pieces is my favorite method.:D

Here’s similar to cjgone’s approach; I prefer working with concrete numbers though.
Let AB=2, BD=4
ABC + CDE = (1/2)(2x2 + 2x1) = 3
ABDF = 2x4 = 8
(8-3)/8 = 5/8
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EDIT
Avoiding fractions:

I drew a line from C to what I called point X (the midpoint of AF)… drawing a line from E to the midpoint of CX and from E to X…

Let AB=BC.
Draw one more line - BX. We have 8 little triangles now of equal area; the shaded part is comprised of 5 of them, thus 5/8.