Darren wrote:
Subject: I'm a math nerd
In response to your 1st Random Shite image for this week:

The area of the colored shapes are:
Green triangle: 0.5 x 2 x 5 = 5 squares
Red triangle: 0.5 x 3 x 8 = 12 squares
Green hexagon: 8 squares
Yellow hexagon: 7 squares
The combined area: 5 + 12 + 8 + 7 = 32 squares

The 3 different sized triangles different slopes:
The green triangle has a slope of 2/5 (rise/run)
The red triangle has a slope of 3/8
The "multi-colored" triangles have a slope of 5/13

Because of the way the first shape is set up, the top of the "triangle" is concave (it bows inward).

If a straight line was drawn from the upper right corner to the lower left, there would be an "empty" gap of 0.5 squares. THUS, the first "triangle" has an area of 32 squares, although it appears to have an area of 32.5 squares (0.5 x 8 x 5).

Because of the way the second shape is set up, the top of the "triangle" is convex (it bows outward).

If a straight line was drawn from the upper right corner to the lower left, there would be a "filled in" gap of 0.5 square units. THUS, the second "triangle" has an area of 33 squares (with the "extra" square), although it appears to have an area of only 32.5 squares (0.5 x 8 x 5).

This is a visual representation of a common error in 4th grade arithmetic when students add fractions with unlike denominators: a/b + c/d = (a+c)/(b+d).

I'm sure you have enough math geeks who visit your site who will give you a
better description than I have. But hopefully this helps.