Sample Problem

Look at the figure below. The shaded area is 53 cm2. What is the area of the square?



If we want to get the area of the square, we have to get the relationship of the square’s area and the shaded area. We do this by ‘dissecting’ the figure into triangles and a rectangle by drawing lines parallel to the square as shown.

We see that there are rectangles that are formed on the four corners of the square. In each rectangle on the four corners, we see that the half is shaded and the other half is white. Thus the shaded area contains the middle rectangle, making it 3 × 2 = 6 cm bigger than the white one. Therefore, the area of the square is (53 - 6) × 2 + 6 = 100 cm2.