Question

The coordinates of the vertices of a polygon are (0,3), (2,3) (2,0), (1,-4) and (-2,-1).

What is the perimeter of the polygon to the nearest tenth of a unit?


A.) 15.8 units


B.) 16.9 units


C.) 17.8 units


D.) 18.6 units

Answer 1

For anyone reading in the future, it is 17.8 units.

Answer 2

Let the cordinates be A(0,3), B(2,3), C(2,0), D(1,-4) and E(-2,-1), then

The perimeter is the sum of the lengths of the line segments joining the coordinates.
Length of AB = 2 units
Length of BC = 3 units
Length of CD = sqrt((1 - 2)^2 + (-4)^2) = sqrt(1 + 16) = sqrt(17) = 4.12 units
Length of DE = sqrt((-1 - (-4))^2 + (-2 - 1)^2) = sqrt(3^2 + (-3)^2) = sqrt(9 + 9) = sqrt(18) = 4.24 units
Length of EA = sqrt((0 - (-2))^2 + (3 - (-1))^2) = sqrt(2^2 + 4^2) = sqrt(4 + 16) = sqrt(20) = 4.47

Therefore, perimeter = 2 + 3 + 4.12 + 4.24 + 4.47 = 17.8 units.