Wednesday, July 18, 2012 1:28:38 PM
It's all in the slope. If you imagine the blue trapezoid as a 3x5 blue square attached to a 2x5 blue triangle, it makes sense. The red triangle has a slope of 3/8 (or 15/60). The blue triangle has a slope of 2/5 (or 16/60). This means that the hypotenuse of the 5x13 "triangle" they form is not a straight line, but bulges inward.
The area of this bulge is a triangle whose sides are the hypotenuses of the red, blue, and 5x13 triangle. If you use the pythagorean theorem to find the value of each hypotenuse (e.g. the hypotenuse of the red triangle is sqrt(3^2+8^2)=8.544), you can then plug those values into Heron`s formula (look it up if for some reason you don`t know it yet still care) to find the area of the triangle, which is 0.5. Do the same thing for the green triangle and orange trapezoid, which have the same dimensions, and you`ll get another 0.5.