Construct a quadrilateral $A B C D$ in which $A B = 5 c m, B C = 6 c m, C D = 4 c m, A D = 3 c m$ and diagonal $A C = 5 c m .$

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Solution

$\Rightarrow$ Draw a line segment AB = 5cm.
$\Rightarrow$ With A as a center and radius AC = 5cm, draw an arc.
$\Rightarrow$ With B as a center and radius BC = 6cm, draw an arc, intersecting the previous arc at point C.
$\Rightarrow$ With A as a center and radius AD = 3cm, draw an arc.
$\Rightarrow$ Take C as a center with radius CD = 4cm draw an arc intersecting the previous arc at point D.
$\Rightarrow$ Join AC, BC, AD and CD.
Thus, ABCD is a required quadrilateral.

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A B C D

A B = 3 c m, B C = 4 c m, C D = 4 c m, D A = 5 c m

A C = 5 c m

Question 2
Find the area of a quadrilateral ABCD in which AB=3cm,BC=4cm,CD=4cm, DA = 5cm and AC= 5cm.

A B C D

A B = 5 c m, B C = 4 c m; C D = 7 c m, A D = 6 c m

B D = 5 c m

A (□ A B C D)

4 (3 + \sqrt{6}) c m^{2}

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