Question

In the following figure, what is the ratio of the areas of

1. shaded portion I to shaded portion II?
   
2. shaded portion II to shaded portion III?
3. shaded portions I and II taken together and shaded portion III?

Answer 1

Area of square = Side × Side

Area of rectangle = Length × Breadth

From the above figure, we can say that

AB = AE – BE = 10 – 5 = 5

BI = EF = AJ = AD + DJ = 5 + 2 = 7

FG = HJ = 3

FI = BE = 5

DC = IJ = AB = 5

DC = IJ = AB = 5

CI = DJ = 2

BC = AD = 5

Now, area of I portion = Area of ABCD

= AB × BC

= 5 × 5

= 25 sq units

Area of III portion = Area of BEFI

= BF × EF

= 5 × 7

= 35 sq units

Area of II portion = Area of DCIJ + Area of FGHI

= DC × CI + GH × HJ

= 5 × 2 + 10 × 3

= 10 + 30

= 40 sq units

a. Ratio of shaded portion I to shaded portion II

= `25/40`

= `5/8`

= 5 : 8

b. Ratio of shaded portion II to shaded portion III

= `40/35`

= `8/7`

= 8 : 7

c. Ratio of shaded portion I and II taken together to shaded portion III

= `(25 + 40)/35`

= `65/35`

= `13/7`

= 13 : 7