Solutions to area of shaded region of rectangle

These are the solutions to the area of the shaded region problem. Register/Login to view. 

Solution 1

All the shaded and unshaded triangles have the same height. The total of their bases is also equal. So, the total area of the unshaded triangle is equal to the total area of the shaded triangle. That’s what the outrageous algebra below is actually saying.

Solution 2

Another trick is to construct parallelograms half of the area of each of which is the shaded part and the other half is the unshaded part.

You know that opposite sides of parallelograms are equal. In the diagram below, p = 11 – (q+r+s).

The answer is not half. The answer is half of 5×11 🙂