Draw a quadrilateral of sides 2cm ,3cm,4cm,6cm and diagonal 5cm. Draw a square with area equal to that of the quadrilateral .H ow can we construct such a figure?

Steps of construction of a quadrilateral when four sides and one of its diagonal are given.
Let AB = 3 cm , AD = 4 cm , BC = 2 cm,CD = 6 cm
We have choosen the sides in such a way that the triangle law of inequality holds .
Step 1 Draw a line BD = 5 cm (length of the diagonal)
Step 2 Draw an arc with centre B and radius = 3 cm .
Step 3 .Draw an arc with centre C and radius = 4 cm meeting previous arc at A.
Step 4 .Similarly on the opposite side of the diagonal,draw arcs with centre at B and D having radius 2 cm and 6 cm respectively.
Let these meet at C.
Hence ABCD is the required quadrilateral.

area of square = area of quadrilateral ABCDAnd area of quad ABCD = area ABD +areaBCDarea ABD = s(s-a)(s-b)(s-c) =6(6-3)(6-4)(6-5)=6×3×2×1=6 sq unitsarea BCD =  s(s-a)(s-b)(s-c)=132×(132-2)(132-5)(132-6)=132×92×32×12=4.68 sq unitsarea of square = 6sq units +4.68 sq units = 10.68 sq unitsHence side of square = 10.68 sq units=3.26 units 


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