Solution
- The coordinates of the points read from the graph given are:
A=(-2,3)
B=(0,6)
C=(5,4)
D=(3,-1)
E=(-1,-2)
- To find the perimeter, we can use the distance between two points formula to find the lengths of each side of the polygon after which we add them up.
- Thus, we have:
[tex]\begin{gathered} D=\sqrt{(y_2-y_1)^2+(x_2-x_1)^2}\text{ \lparen Distance between two points\rparen} \\ \\ AB=\sqrt{(6-3)^2+(0--2)^2} \\ AB=\sqrt{9+4}=\sqrt{13} \\ \\ BC=\sqrt{(6-4)^2+(0-5)^2} \\ BC=\sqrt{4+25}=\sqrt{29} \\ \\ CD=\sqrt{(4--1)^2+(5-3)^2} \\ CD=\sqrt{25+4}=\sqrt{29} \\ \\ DE=\sqrt{(-2--1)^2+(-1-3)^2} \\ DE=\sqrt{1+16}=\sqrt{17} \\ \\ AE=\sqrt{(3--2)^2+(-2--1)^2} \\ AE=\sqrt{25+1}=\sqrt{26} \end{gathered}[/tex]
- Thus, the Perimeter is
[tex]\begin{gathered} P=AB+BC+CD+DE+AE \\ P=\sqrt{13}+\sqrt{29}+\sqrt{29}+\sqrt{17}+\sqrt{26} \\ P=23.598006...\approx24units \end{gathered}[/tex]
- Thus the best approximation is 24.3 units (OPTION B)
