Geometry

Question Analysis

The main focus is to find the lengths of each side of the hexagon and sum them up to calculate the perimeter. Since all sides are either horizontal or vertical, we can use the absolute difference of coordinates to find their lengths.

 

Key Concept Explanation

For horizontal sides (where - coordinates of two endpoints are the same), the length is . For vertical sides (where - coordinates of two endpoints are the same), the length is . The perimeter of a polygon is the sum of the lengths of all its sides.

 

Step - by - Step Solution

1. Length of :

Since and (horizontal side), .

2. Length of :

Since and (vertical side), .

3. Length of :

Since and (horizontal side), .

4. Length of :

Since and

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