P4 Math: Rectangles and Square

The figure below is made up of Rectangle P, Rectangle Q, Rectangle R, and Square S. The perimeter of rectangle Q is 40 cm. The perimeter of the figure is 72 cm.

(a) Find the length of AB.

(b) Find the area of Square S.

Solution:

Mark the figure edges to find its perimeter.

Few tricks needed here to shift (imaginary) two sides of rectangle Q since the before and after length are same. Color the edges with sky blue.

20 + 20 = 40 cm

Now, from figure perimeter there is only left (72 - 40) cm = 32 cm not mapped in the figure. Color the edges with green.

4u = 32, u = 8 

(a) So length AB = 8

(b) Area of Square S = uxu = 8x8 = 64 cm²