MATH SOLVE

2 months ago

Q:
# 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

Accepted Solution

A:

Answer:20.76 unitsStep-by-step explanation:The distance between the points (-4,2) and (2,2) is [tex]\sqrt{(-4-2)^{2} +(2-2)^{2} } = 6[/tex] units.Now, distance between the points (2,2) and (2,-1) is [tex]\sqrt{(2-2)^{2} +(2-(-1))^{2} } = 3[/tex] units.Again the distance between the points (2,-1) and (-2,-3) is [tex]\sqrt{(2-(-2))^{2}+(-1-(-3))^{2} Β } = \sqrt{20}[/tex] units.Now, the distance between the points (-2,-3) and (-5,-2) is [tex]\sqrt{(-2-(-5))^{2}+(-3-(-2))^{2} Β } = \sqrt{10}[/tex] units.Again the distance between the points (-5,-2) and (-4,2) is [tex]\sqrt{(-5-(-4))^{2} +(-2-2)^{2} } =\sqrt{17}[/tex]Therefore, the perimeter of the polygon is (6 + 3 + β20 + β10 + β17) = 20.76 units {Rounded to the nearest tenth of the unit} (Answer)