# 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

Aug 23, 2017

Option C. $17.8 \text{ units}$

#### Explanation:

As shown in th figure, $A B C D E$ is the polygon.
perimeter of the polygon $p = A B + B C + C D + D E + E A$
As $A B$ is a horizontal line, $\implies A B = | 2 - 0 | = 2$
As $B C$ is a vertical line, $\implies B C = | 0 - 3 | = 3$
Use the distance formula to find $C D , D E \mathmr{and} E A$
$C D = \sqrt{{\left(1 - 2\right)}^{2} + {\left(- 4 - 0\right)}^{2}} = \sqrt{1 + 16} = \sqrt{17}$
$D E = \sqrt{{\left(- 2 - 1\right)}^{2} + {\left(- 1 - \left(- 4\right)\right)}^{2}} = \sqrt{9 + 9} = \sqrt{18}$
$E A = \sqrt{{\left(0 - \left(- 2\right)\right)}^{2} + {\left(3 - \left(- 1\right)\right)}^{2}} = \sqrt{4 + 16} = \sqrt{20}$

$\implies$ perimeter $p = 2 + 3 + \sqrt{17} + \sqrt{18} + \sqrt{20} \approx 17.8$ units