Geometry

Question Analysis

The main focus is using the coordinates of the rectangle's vertices to find the length of its sides and then applying the formula for the area of a rectangle, , where  is the length and  is the width.

Key Concept Explanation

The area of a rectangle is calculated by the formula , where  is the length and  is the width. In a coordinate plane, when two points have the same  - coordinate, the difference in their  - coordinates gives the vertical distance between them. When two points have the same  - coordinate, the difference in their  - coordinates gives the horizontal distance between them.

Step - by - Step Solution

1. Find the length of the vertical sides:

Points  and  have the same  - coordinate. The length of the vertical side (width ) is the absolute value of the difference in their  - coordinates: