Answer :

The perimeter of the quadrilateral is approximately 50.47 units

  • A quadrilateral is polygon which has 4 sides.
  • The perimeter of a quadrilateral is the sum of the side - lengths of all sides of the quadrilateral .
  • the side lengths are calculated by using the distance formula between two points on the cartesian plane which is given by [tex]{\displaystyle d={\sqrt {(x_{2}-x_{1})^{2}+(y_{2}-y_{1})^{2}}}.}[/tex]

Given the vertices of the quadrilateral: H(– 4,6), I(4,9), J(2,3), K(7, – 4).

Let us calculate the distances of HI , IJ , JK and KH

[tex]{\displaystyle HI={\sqrt {(4-(-4))^{2}+(9-(6))^{2}}}.}[/tex]

or, HI = 17 units

[tex]{\displaystyle IJ={\sqrt {(2-(4))^{2}+(3-(9))^{2}}}.}[/tex]

or, IJ = 10

[tex]{\displaystyle JK={\sqrt {(7-(2))^{2}+(-4-(3))^{2}}}.}[/tex]

or, JK = √74 = 8.602... ≈ 8.60

[tex]{\displaystyle KH={\sqrt {(7-(-4))^{2}+(-4-(6))^{2}}}.}[/tex]

or, KH = √221 = 14.866... ≈ 14.87

Now perimeter = HI + IJ + JK + KH

or, perimeter = 8.60 + 14.87 + 10 + 17 = 50.47 units.

Therefore the perimeter of the quadrilateral is 50.47 units.

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