Easy, the hypotenuse lines are different. It appears that one is curved outware while the other is curved inward.
~wartex8

red: 12
green: 5
blue: 6 + 2 = 8
yellow: 4 + 3 = 7

red + green + blue + yellow = 32 = RGBY

area rect: 13 times 5 = 65 = A

RGBY = .5(A - 1)

The triangle formed by RGBY appears to be half the area
of the rectangle when it is actually half of 1 less than the area
of the rectangle that is, RGBY = .5(A - 1). Hence, the extra block.

The area of the triangle is .5(BH) that is, half of the area of the rectangle, BH,
formed by the triangle.

The area RGBY is given by .5(A - 1), shown above.

If the area of RGBY were actually half the area of the rectangle A then,

.5(BH) = .5(A - 1) => BH = A - 1 => A = BH - 1

This implies that the area of the rectangle A must be BH - 1.

This a contradiction since, the area of the rectangle is BH not BH - 1.

Numerically,

RGBY = 12 + 5 + 8 + 7 = 32,

given by the area of the shapes colored red, green, blue, and yellow respectively.

The area of the rectangle A = 13 x 5 = 65,

given by the length times the width of the rectange.

By definition the area of a trianle is half the area of the rectangle formed by it.

32 is not half of 65.

So,

The rectangle A is not formed by the triangle RGBY.

Half of the area of the rectangle is 32.5 square units; the shaded area is equal to 32. It doesn't really take up half of the rectangle (except optically), so when you move the shaded pieces around, the difference is more obvious. Am I on the right track?

Linda Jo