Question

The coordinates of the vertices of a polygon at (-4,2),(2,2),(2,-1),(-2,-3) and (-5,-2). What is the perimeter of the polygon. Enter your answer as a decimal,rounded to the nearest tenth of a unit

Answer 1

20.76 units

Explanation:

The distance between the points (-4,2) and (2,2) is
`\sqrt{(-4-2)^(2) +(2-2)^(2) } = 6` units.

Now, distance between the points (2,2) and (2,-1) is
`\sqrt{(2-2)^(2) +(2-(-1))^(2) } = 3` units.

Again the distance between the points (2,-1) and (-2,-3) is
`\sqrt{(2-(-2))^(2)+(-1-(-3))^(2)  } = √(20)` units.

Now, the distance between the points (-2,-3) and (-5,-2) is
`\sqrt{(-2-(-5))^(2)+(-3-(-2))^(2)  } = √(10)` units.

Again the distance between the points (-5,-2) and (-4,2) is
`\sqrt{(-5-(-4))^(2) +(-2-2)^(2) } =√(17)`

Therefore, the perimeter of the polygon is (6 + 3 + √20 + √10 + √17) = 20.76 units {Rounded to the nearest tenth of the unit} (Answer)