Pei Chun Public School PSLE Math Prelim 2007 Question

Rectangles X and Y are overlapped as shown in the figure below. The ratio of the area of the rectangle X to that of rectangle Y is 3 : 5. The ratio of the unshaded area of rectangle X to the unshaded area of rectangle Y is 1 : 3. The dimension of rectangle X is 6cm by 4cm.

(a) What is the area of the shaded part?
(b) What is the fraction of the area of the shaded part to that of the whole figure?



Working Solution -

The ratio of the unshaded area of rectangle X to the unshaded area of rectangle Y is 1 : 3. Hence, we label 1 unit for unshaded area of rectangle X and 3 units for unshaded area of rectangle Y as shown below.


We also know that the ratio of the area of rectangle X to that of rectangle Y is 3 : 5

For area of rectangle X to that of rectangle Y to be 3 : 5, the shaded area has to be 2 units as illustrated in the figure below.



We also know that Area of Rectangle X is

6 cm (length) x 4 cm (breadth) = 24 square centimetres.

Ratio of Area of rectangle X to that of Area of rectangle Y is 3 : 5

(Area X) is 3 units ----- 24 square centimetres.

1 unit ----- 24 square centimetres divided by 3 = 8 square centimetres.
(The all important 1 unit)



Q(a) What is the area of the shaded part?

Area of shaded part is
2 units ------- 8 square centimetres x 2 = 16 square centimetres

Answer: The area of the shaded part is 16 square centimetres.



Q(b) What is the fraction of the area of the shaded part to that of the whole figure?

Shaded part ----- 2 units
Whole figure ------ 1 unit (unshaded part of rectangle X) + 3 units (unshaded part of rectangle Y) + 2 units (shaded part) = 6 units

Area of unshaded part / Area of whole figure.

2 units / 6 units = 1/3

Answer: The fraction of the area of the shaded part to that of the whole figure is 1/3.