Construct a quadrilateral $P Q R S$ in which $P Q = 3.5 c m, Q R = 5.5 c m, P S = 4.5 c m, Q S = 5.5 c m$ and $S R = 4.5 c m$ .

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Solution

$\Rightarrow$ Draw a line segment $P Q = 3.5 c m$
$\Rightarrow$ Take $P$ as center with radius $4.5 c m$ and draw an arc.
$\Rightarrow$ Take $Q$ as center with radius $5.5 c m$ and draw an arc, which cuts off previous arc at point $S$
$\Rightarrow$ Take $Q$ as center with radius $5.5 c m$ and draw an arc.
$\Rightarrow$ Take $S$ as center with radius $4.5 c m$ and draw an arc, which cuts off previous arc at point $R$
$\Rightarrow$ Join $P S, Q S, Q R$ and $S R$
$∴$ $P Q R S$ is required quadrilateral.

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(i) Quadrilateral $A B C D$

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