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 vertices A, B, C, D, and E, we need to calculate the lengths of the sides connecting these points and then sum those lengths.

The coordinates of the points are:
- A = (-1, -2)
- B = (-2, 0)
- C = (0, 2)
- D = (2, 0)
- E = (1, 2)

We can determine the length between two points \((x_1, y_1)\) and \((x_2, y_2)\) using the distance formula:

\[
d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
\]

Now, we will calculate the distance between each pair of adjacent vertices:

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

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

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

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

5. **E to A**:
\[
d_{EA} = \sqrt{((-1) - 1)^2 + ((-2) - 2)^2} = \sqrt{(-2)^2 + (-4)^2} = \sqrt{4 + 16} = \sqrt{20} \approx 4.5
\]

Now, we sum the lengths to find the perimeter:

\[
\text{Perimeter} = d_{AB} + d_{BC} + d_{CD} + d_{DE} + d_{EA} \approx 2.2 + 2.8 + 2.8 + 2.2 + 4.5
\]

Calculating the total:

\[
\text{Perimeter} \approx 2.2 + 2.8 + 2.8 + 2.2 + 4.5 = 14.5
\]

Thus, the perimeter of the polygon is approximately **14.5 units**.