Question

The coordinates of the vertices of a polygon are (−2,1), (−3,3), (−1,5), (2,4), and (2,1).

Answer 1

$\sqrt{5} + 2 \sqrt{2} + \sqrt{10} + 3 + 4 \\ = 2.24 + 2.83 + 3.16 + 3 + 4 \\ = 8.23 + 7 = 15.23$
So the best rounded answer to nearest tenth is: A) 15.2 units

Answer 2

Name them as vertices A,B,C , D and E in that order.

$ab = \sqrt{ {( - 2 + 3)}^{2} + (1 - 3)^{2}} = \sqrt{5} \\ bc = \sqrt{ {( - 3 + 1)}^{2} + {(3 - 5)}^{2} } = 2 \sqrt{2} \\ cd = \sqrt{ { (- 1 - 2)}^{2} + {(5 - 4)}^{2} } = \sqrt{10} \\ de = \sqrt{ {(2 - 2)}^{2} + {(4 - 1)}^{2} } = 3 \\ ea = \sqrt{ {(2 + 2)}^{2} + {(1 - 1)}^{2} } = 4 \\ peimeter = ab + bc + cd + de + ea = 15.227 \: or \: 15.23$