The figure is not drawn to scale. It is made up of a square and a rectangle. The ratio of the area of the square to that of the rectangle is 8 : 11. After the shaded part is cut out, the ratio of the area of unshaded part of the rectangle to that of the unshaded part of the square is 7 : 4. Given the length of the square is 8 cm, find the area of the shaded part.

	Square	Rectangle	Difference
Before	8 u	11 u	3 u
Change	- 4 u	- 4 u
After	4 u	7 u	3 u

The shaded area of the square is the same as the shaded area of the rectangle. 

The difference in the areas of the square and the rectangle before and after the shaded part is cut out remains the same.

Area of the square
= 8 x 8
= 64 cm²

8 u = 64

1 u = 64 ÷ 8 = 8

Area of the shaded part
= 4 u
= 4 x 8
= 32 cm²

Answer(s): 32 cm²