Solved Examples: Finding Area of Rectangles on a Coordinate Plane (Grade 6)

📐 Quick Study Guide

• 📍 Coordinate Plane Basics: The coordinate plane is formed by two perpendicular number lines: the x-axis (horizontal) and the y-axis (vertical). Points are located using ordered pairs (x, y).
• 📏 Finding Side Lengths: To find the length of a side of a rectangle on the coordinate plane, count the units between the coordinates. If the coordinates share the same x-value, you are finding the vertical length. If they share the same y-value, you are finding the horizontal length.
• ➕ Absolute Value: Remember to use absolute values when finding the distance between points if you have negative coordinates. The distance is always a positive number!
• 📝 Area Formula: The area of a rectangle is calculated by multiplying its length (l) by its width (w): $Area = l \times w$.
• 🔢 Units: Always include the appropriate units (e.g., square units, units$^2$) when stating the area.

✍️ Practice Quiz

1. What is the area of a rectangle with vertices at (1, 2), (1, 5), (4, 2), and (4, 5)?
   1. 6 square units
   2. 9 square units
   3. 12 square units
   4. 15 square units
2. A rectangle has vertices at (-2, -1), (-2, 3), (3, -1), and (3, 3). What is its area?
   1. 8 square units
   2. 15 square units
   3. 20 square units
   4. 25 square units
3. What is the length of the side connecting (0, -4) and (0, 2)?
   1. 2 units
   2. 4 units
   3. 6 units
   4. 8 units
4. A rectangle has a length of 7 units and a width of 4 units. What is its area?
   1. 11 square units
   2. 14 square units
   3. 21 square units
   4. 28 square units
5. Points (5, 1) and (5, 6) represent one side of a rectangle. Points (2, 1) and (2, 6) represent the opposite side. What is the area of the rectangle?
   1. 10 square units
   2. 12 square units
   3. 15 square units
   4. 18 square units
6. One side of a rectangle is defined by points (-3, 0) and (5, 0). Another side is defined by (-3, 4) and (5, 4). What is the rectangle's area?
   1. 12 square units
   2. 24 square units
   3. 32 square units
   4. 40 square units
7. A rectangle has vertices (1, -1), (1, -5), (6, -1), and (6, -5). What is its area?
   1. 9 square units
   2. 16 square units
   3. 20 square units
   4. 25 square units