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The coordinates of the vertices of a polygon are (−2,1), (−3,3), (−1,5), (2,4), and (2,1).
   
What is the perimeter of the polygon to the nearest tenth of a unit?

15.2 units

15.9 units

16. 5 units

18.8 units

Verified Answer :

Answer: The correct option is A. The perimeter of the polygon is 15.2 units.

Explanation:

The perimeter of a shape is the sum of its all sides.

Let the vertices of the polygon be ABCDE.

\(\text{perimeter}=AB+BC+CD+DE+AD\)

Use distance formula to find the length of sides.

\(D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

\(AB=\sqrt{(3-1)^2+(-3+2)^2}=\sqrt{4+1}=\sqrt{5}\)

\(BC=\sqrt{(5-3)^2+(-1+3)^2}=\sqrt{4+4}=\sqrt{8}\)

\(CD=\sqrt{(4-5)^2+(2+1)^2}=\sqrt{1+9}=\sqrt{10}\)

\(DE=\sqrt{(1-4)^2+(2-2)^2}=\sqrt{9+0}=3\)

\(AE=\sqrt{(1-1)^2+(-2-2)^2}=\sqrt{0+16}=4\)

So, the length of sides are \(\sqrt{5},\sqrt{10},\sqrt{8}, 3,4\)

\(\text{perimeter}=\sqrt{5}+ \sqrt{10}+ \sqrt{8}+ 3+4\)

\(\text{perimeter}=2.23+3.16+2.83+7\)

\(\text{perimeter}=15.22\)

When we Approx 15.22 to nearest tenth, we get 15.2.

Therefore, A is the correct option.

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hamfam2419

Answer:

15.2 units

Step-by-step explanation:

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