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 x_{2} = 1,y_{2} = – 2,x_{1} = 0,y_{1} = 0

∴ AB =

∴ AB =

∴ AB =

**∴** **AB = √5unit**

BC = distance between point B and C =

Here x_{2} = – 3,y_{2} = – 2,x_{1} = 1,y_{1} = – 2

∴ BC =

∴ BC =

∴ BC =

**∴** **BC = 2 units**

CD = distance between point C and D =

Here x_{2} = – 3,y_{2} = 1,x_{1} = – 3,y_{1} = – 2

∴ CD =

∴ CD =

∴ CD =

**∴** **CD = 3 units**

DA = distance between point D and A =

Here x_{2} = 0,y_{2} = 0,x_{1} = – 3,y_{1} = 1

∴ DA =

∴ DA =

∴ DA =

**∴** **DA = √10 units**

Length of diagonal

AC = distance between point A and C =

Here x_{2} = – 3,y_{2} = – 2,x_{1} = 0,y_{1} = 0

∴ AC =

∴ AC =

∴ AC =

**∴** **AC = √13 units**

Length of diagonal

BD = distance between point B and D =

Here x_{2} = – 3,y_{2} = 1,x_{1} = 1,y_{1} = – 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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