Question

A=-1-2
B=-2,0
C=0,2
D=2,0
E=1,-2
Using the coordinates, what is the perimeter of the polygon? Round each calculation to the nearest tenth

Answer 1

To find the perimeter of the polygon with the given coordinates, we first identify the coordinates for each point:

- A = (-1, -2)
- B = (-2, 0)
- C = (0, 2)
- D = (2, 0)
- E = (1, -2)

Next, we will calculate the distance between each pair of consecutive points to find the lengths of the sides of the polygon. We'll also include the distance between the last point E and the first point A to close the polygon.

The distance \(d\) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is calculated using the distance formula:
\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Now, let's calculate the distances:

1. Distance between A and B:
\[
d_{AB} = \sqrt{((-2) - (-1))^2 + (0 - (-2))^2} = \sqrt{(-1)^2 + (2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.2
\]

2. Distance between B and C:
\[
d_{BC} = \sqrt{(0 - (-2))^2 + (2 - 0)^2} = \sqrt{(2)^2 + (2)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.8
\]

3. Distance between C and D:
\[
d_{CD} = \sqrt{(2 - 0)^2 + (0 - 2)^2} = \sqrt{(2)^2 + (-2)^2} = \sqrt{4 + 4} = \sqrt{8} \approx 2.8
\]

4. Distance between D and E:
\[
d_{DE} = \sqrt{(1 - 2)^2 + (-2 - 0)^2} = \sqrt{(-1)^2 + (-2)^2} = \sqrt{1 + 4} = \sqrt{5} \approx 2.2
\]

5. Distance between E and A:
\[
d_{EA} = \sqrt{((-1) - 1)^2 + (-2 - (-2))^2} = \sqrt{(-2)^2 + (0)^2} = \sqrt{4} = 2.0
\]

Now we sum all the calculated distances to find the perimeter:
\[
\text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DE} + d_{EA}
\]
\[
\text{Perimeter} \approx 2.2 + 2.8 + 2.8 + 2.2 + 2.0 \approx 12.0
\]

Thus, the perimeter of the polygon is approximately **12.0**.