Question

Question 77

In figure, what is the ratio of the areas of

a) shaded portion I to shaded portion II?

b) Shaded portion II to shaded portion III?

c) The shaded portion I and II taken together and shaded portion III?

Answer 1

Area of square = Side $\times$ Side

Area of Rectangle = Length $\times$ 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
DC = IJ = AB = 5
CI = DJ = 2
BC = AD = 5
Now, area of portion I = Area of ABCD
$=AB\times BC=5\times 5=25sq.units$

Area of III portion = Area of BEFI
$=BE\times EF=5\times 7=35sq.units$

Area of II portion = Area of DCIJ + Area of FGHJ
= $DC\times CI+GH\times HJ$
= $5\times 2+10\times 3$
= $10+30$
= $40squnits$

a) Ratio of shaded portion I to shaded portion II $=\frac{25}{40}=\frac{5}{8}=5:8$

b) Ratio of shaded portion II to shaded portion III $=\frac{40}{35}=\frac{8}{7}=8:7$

c) Ratio of shaded portion I and II taken together to shaded portion III $=\frac{25+40}{35}=\frac{65}{35}=\frac{13}{7}=13:7$