# Area of a Convex Polygon

Simple+

There is a convex polygon on a coordinate plane. This polygon is presented as a list of vertices coordinates. Each vertex is connected sequentially with the last connecting back to the first. A polygon has N vertices. You should write a program that will calculate the area of a polygon. The result should be given with one digits precision as ±0.1.

Input: Coordinates as a list of lists. Each list contains two integers.

Output: The area of the polygon as a float.

Example:

```checkio([[1, 1], [9, 9], [9, 1]]) == 32
checkio([[4, 10], [7, 1], [1, 4]]) == 22.5
checkio([[1, 2], [3, 8], [9, 8], [7, 1]]) == 40
checkio([[3, 3], [2, 7], [5, 9], [8, 7], [7, 3]]) == 26
checkio([[7, 2], [3, 2], [1, 5],
[3, 9], [7, 9], [9, 6]]) == 42
checkio([[4, 1], [3, 4], [3, 7], [4, 8],
[7, 9], [9, 6], [7, 1]]) == 35.5```

How it is used: This concept is very useful in topography and architecture. You can improve the algorithm and calculate the area of any zone on the map taking into account elevation and other points of interest. You could also use this idea to construct something like a building, or a boat.

Precondition: 3 ≤ N ≤ 8
∀ x, y ∈ coordinates : 0 ≤ x ≤ 10; 0 ≤ y ≤ 10;

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CheckiO Extensions

CheckiO Extensions allow you to use local files to solve missions. More info in a blog post.

In order to install CheckiO client you'll need installed Python (version at least 3.8)

Install CheckiO Client first:

`pip3 install checkio_client`

`checkio --domain=py config --key=`

Sync solutions into your local folder

`checkio sync`

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`checkio serv -d`

Alternatevly, you can install Chrome extension or FF addon

`checkio install-plugin`
`checkio install-plugin --ff`
`checkio install-plugin --chromium`

Read more here about other functionality that the checkio client provides. Feel free to submit an issue in case of any difficulties.

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