**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.**

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