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

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.