Q. 13.7( 3 Votes )

Calculate the length of the sides and diagonals of the quadrilateral below:


Answer :

Let A = (0,0)


B = (1, – 2)


C = (– 3, – 2)


D = (– 3,1)


Here, AB, BC, CD, DA are the sides of the quadrilateral and AC and BD are the diagonals of the quadrilateral.


Length of Side


AB = distance between point A and B =


Here x2 = 1,y2 = – 2,x1 = 0,y1 = 0


AB =


AB =


AB =


AB = √5unit


BC = distance between point B and C =


Here x2 = – 3,y2 = – 2,x1 = 1,y1 = – 2


BC =


BC =


BC =


BC = 2 units


CD = distance between point C and D =


Here x2 = – 3,y2 = 1,x1 = – 3,y1 = – 2


CD =


CD =


CD =


CD = 3 units


DA = distance between point D and A =


Here x2 = 0,y2 = 0,x1 = – 3,y1 = 1


DA =


DA =


DA =


DA = √10 units


Length of diagonal


AC = distance between point A and C =


Here x2 = – 3,y2 = – 2,x1 = 0,y1 = 0


AC =


AC =


AC =


AC = √13 units


Length of diagonal


BD = distance between point B and D =


Here x2 = – 3,y2 = 1,x1 = 1,y1 = – 2


BD =


BD =


BD =


BD = 5 units


Hence, length of the sides of the quadrilateral is √5,2,3,√10 units.


Length of the diagonals of the quadrilateral are √13 and 5 units.


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