Geometry

Question Analysis

The main focus is to find the lengths of each side of the pentagon using the distance formula for non - horizontal/vertical sides and simple coordinate differences for horizontal/vertical sides, then sum these lengths to get the perimeter.

Key Concept Explanation

The distance formula between two points and is . For horizontal sides (), the length is , and for vertical sides (), 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 :

For and , use the distance formula:

.

2. Length of :

For and , since - coordinates are the same (horizontal side), .

3. Length of :

For and

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