Yu claims:
A rectangle is a trapezoid. The shaded area (2 equal triangles) = ¼ of the rectangle.
The above trapezoid has the same area as the rectangle above. As P approaches Q, the height of the upper shaded triangle increases faster than the height of the lower shaded triangle decreases. .: the shaded area > ¼ of the trapezoid.
A rectangle is a trapezoid. The shaded area (2 equal triangles) = ¼ of the rectangle.
The above trapezoid has the same area as the rectangle above. As P approaches Q, the height of the upper shaded triangle increases faster than the height of the lower shaded triangle decreases. .: the shaded area > ¼ of the trapezoid. 
"As P approaches Q, the height of the upper shaded triangle increases faster than the height of the lower shaded triangle decreases."
ReplyDeleteis true but there must a mathematical way of making that statement. something like:
PQ gets shorter by dx, then dh1 > dh2.
above can probably be shown.
-binary