Question

The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the polygon to the nearest tenth of a unit.
Do not label your answer. Answer with a number only.

Answer 1

Answer:

Perimeter

$\bf \boxed{7+\sqrt{5}+\sqrt{8}+\sqrt{10}}$

Step-by-step explanation:

Draw the polygon to have an idea of what you are being asked.

See picture attached

Now find the length of each side and add them up, that is the perimeter.

To find the length of a side use the formula of the distance between to points (a,b) and (c,d)

$\bf \sqrt{(a-c)^2+(b-d)^2}$

Distance between (-2,1) and (-3,3)

$\bf \sqrt{(-2-(-3))^2+(1-3)^2}=\sqrt{5}$

Distance between  (-3,3) and (-1,5)

$\bf \sqrt{(-3-(-1))^2+(3-5)^2}=\sqrt{8}$

Distance between  (-1,5) and (2,4)

$\bf \sqrt{(-1-2)^2+(5-4)^2}=\sqrt{10}$

Distance between (2,4) and (2,1) (obviously 3)

$\bf \sqrt{(2-2)^2+(4-1)^2}=3$

Distance between (2,1) and (-2,1) (obviously 4)

$\bf \sqrt{(-2-2)^2+(1-1)^2}=4$

Add up all the lengths

$\bf \sqrt{5}+\sqrt{8}+\sqrt{10}+3+4$

Perimeter

$\bf \boxed{7+\sqrt{5}+\sqrt{8}+\sqrt{10}}$