# Question 6c18b

Jan 23, 2018

Lengths of each side of the polygon are

$\textcolor{b l u e}{a = 5 , b \approx 3.6 , c \approx 3.6 , d \approx 1.4 , e \approx 5.4}$

#### Explanation:

A polygon that does not have all sides equal and all angles equal. A polygon is "regular" only when all angles are equal and all sides are equal, otherwise it is irregular.

Regular Pentagon.

Distance between two points is given by the formula

$d = \sqrt{{\left(x 2 - x 1\right)}^{2} + {\left(y 2 - y 1\right)}^{2}}$

Let the sides be a, b, c, d & e.

$a = \sqrt{{\left(- 3 + 3\right)}^{2} + {\left(2 + 3\right)}^{2}} = \sqrt{25} = 5$

$b = \sqrt{{\left(0 + 3\right)}^{2} + {\left(4 - 2\right)}^{2}} = \sqrt{13} \approx 3.6$

c = sqrt((2-0)^2 + (1-4)^2)) = sqrt 13 ~~ 3.6#

$d = \sqrt{{\left(2 - 2\right)}^{2} + {\left(- 1 - 1\right)}^{2}} = \sqrt{2} \approx 1.4$

$e = \sqrt{{\left(2 + 3\right)}^{1} + {\left(- 1 + 3\right)}^{2}} = \sqrt{29} \approx 5.4$