Question 15 Marks

In Fig., 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.\ $Shaded portions $I$ and $II$ taken together and shaded portion $III?$

Answer

Area of square $=$ Side $\times $ Side Area of Rectangle $=$ Length $\times $ Breadth

 From the above figure, we can say that
$AE = AE - BE = 10 - 5 = 5$
$BI = EF = AJ = AD + DJ$
$= 5 + 2 = 7$
$FG = HJ = 3$
$FI = BE = 5$
$DC = IJ = AB = 5$
$CI = DJ = 2$
$BC = AD = 5$
Now, area of $I$ portion $=$ Area of $ABCD = AB \times BC = 5 \times 5 = 25sq$
units Area of $III$ portion $=$ Area of $BEFI = BF \times EF = 5 \times 7 = 35sq$
units Area of $II$ portion $=$ Area of $DCIJ\ +$ Area of $FGHI = DC \times CI + GH \times HJ = 5 \times 2 + 10 \times 3 = 10 + 30 = 40sq$ units
$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 $III =\frac{25+40}{35}=\frac{65}{35}=\frac{13}{7}=13:7$

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