Question

find the perimeter of the polygon. round your answer to the nearest tenth.

Explanation:

Step1: Find coordinates of points

Assume grid has unit length. Coordinates: \(A(2,0)\), \(B(-4,5)\), \(C(3,10)\), \(D(8,7)\), \(E(4,5)\)

Step2: Use distance formula \(d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\)

• \(AB=\sqrt{(2 + 4)^2+(0 - 5)^2}=\sqrt{36 + 25}=\sqrt{61}\approx7.8\)
• \(BC=\sqrt{(3 + 4)^2+(10 - 5)^2}=\sqrt{49 + 25}=\sqrt{74}\approx8.6\)
• \(CD=\sqrt{(8 - 3)^2+(7 - 10)^2}=\sqrt{25 + 9}=\sqrt{34}\approx5.8\)
• \(DE=\sqrt{(4 - 8)^2+(5 - 7)^2}=\sqrt{16 + 4}=\sqrt{20}\approx4.5\)
• \(EA=\sqrt{(2 - 4)^2+(0 - 5)^2}=\sqrt{4 + 25}=\sqrt{29}\approx5.4\)

Step3: Sum up the lengths

Perimeter \(P=AB + BC+CD + DE+EA\approx7.8+8.6 + 5.8+4.5+5.4 = 32.1\)

Answer:

32.1