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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