I'm sure some (if not most) have seen this by now and since I'm fairly new to real deep mathematical explorations I'm stumped as to why this would be true.

For class I was asked to cut out an 8" x 8" square and then asked to cut the square into 2 right triangles each of base height 3" and base 8" and two trapezoids each of base1 3" and base2 5" with height 5".

I was then asked to rearrange the shapes to make an 5" x 13" rectangle and sure enough the pieces fit snuggly. Now 5" x 13" will not give us the same area that we initially had. Measuring the pieces separately one would get that each trapezoid has an area of 20 inches squared and each triangle has an area of 12 inches squared.

Any explanations please, thank you!