Answer:
The vertices of the hexagon are given as follows:
A (10, 10)
B (20, 10)
C (30, 0)
D (20, -10)
E (10, -10)
F (-10, 0)
To calculate the perimeter, we need to find the lengths of the six sides and add them together.
Side AB:
Using the distance formula, we can calculate the distance between points A and B:
AB = √[(20-10)^2 + (10-10)^2] = √(10^2) = 10 units
Similarly, we can find the lengths of the other sides:
BC = √[(30-20)^2 + (0-10)^2] = √(10^2 + 10^2) = √200 ≈ 14.14 units
CD = √[(20-30)^2 + (-10-0)^2] = √(10^2 + 10^2) = √200 ≈ 14.14 units
DE = √[(10-20)^2 + (-10-(-10))^2] = √(10^2) = 10 units
EF = √[(-10-10)^2 + (0-(-10))^2] = √(20^2 + 10^2) = √500 ≈ 22.36 units
FA = √[(10-(-10))^2 + (10-0)^2] = √(20^2 + 10^2) = √500 ≈ 22.36 units
Now, we add up the lengths of all the sides to find the perimeter:
Perimeter = AB + BC + CD + DE + EF + FA = 10 + 14.14 + 14.14 + 10 + 22.36 + 22.36 ≈ 93 units
To find the area of the hexagon, we can split it into two triangles, ABC and DEF, and calculate their individual areas using the Shoelace Formula or other methods. However, since the hexagon is not a regular shape and its coordinates are not aligned in a way that makes calculation easy, we cannot determine its area without further information or additional measurements.
Therefore, the perimeter of hexagon ABCDEF is approximately 93 units, but the area cannot be determined with the given information.