Question

In a floral design made from square tiles each of dimensions 40 cm by 40 cm (See figure), find the ratios of

a) The perimeter of the shaded portion to the perimeter of the whole design.

b) The area of the shaded portion to the area of the unshaded portion.

Answer 1

From the above figure, we find that:

Perimeter of shaded portion = 10 units
Perimeter of whole design = 18 units
Area of shaded portion = 6 sq. units
Area of whole design = 20 sq. units

Also, area of unshaded portion = Total area - Area of the shaded portion

= 20 - 6 = 14 sq. units

a) Ratio of perimeter of the shaded portion to the perimeter of the whole design

= $\frac{\text{Perimeter of shaded portion}}{\text{Perimeter of whole design}}$

= $\frac{10}{18}$
= $\frac{5}{9}=5:9$ [on dividing numerator and denominator by 2]

b) Ratio of area shaded portion to the area of unshaded portion

= $\frac{\text{Area of shaded portion}}{\text{Area of unshaded portion}}$

= $\frac{6}{20-6}$

= $\frac{6}{14}=\frac{3}{7}=3:7$ [on dividing numerator and denominator by 2]