Area of Rectangle on the Coordinate Plane Game

Area of Rectangle on the Coordinate Plane Game
To play Coordinate Cadet: Area Architect, you must take on the role of a geometric surveyor. Your goal is to determine the area of rectangular “plots” using coordinate data. Scroll down the page for a more detailed explanation.
 

 

How to Play the Area of Rectangle on the Coordinate Plane Game
Step 1: Choose Your Mission
When you launch the game, you must select one of two difficulty levels:
Survey Standard: You will see a visual grid with the shape drawn out. This is best if you prefer to visualize the space.
Survey Tactical: The grid is hidden. You are given only the (x, y) coordinates. You must use mental math to find the dimensions.
Survey Elite: The most difficult mode. The rectangles are rotated, meaning you would need to use the Distance Formula.

Step 2: Calculate the Area
Once the mission begins, you are presented with four vertices (corners) labeled V1 through V4. Since these are always rectangles, you need to find the Width and Height.

How to calculate from coordinates:

1. Basic Plots (Standard/Tactical)
   Find the Width: Look at two vertices where the y value is the same. Subtract their x values.
   Example: If V1 is (2, 2) and V2 is (5, 2), the width is 3 (5 - 2 = 3).
   Find the Height: Look at two vertices where the x value is the same. Subtract their y values.
   Example: If V1 is (2, 2) and V4 is (2, 6), the height is 4 (6 - 2 = 4).
   Find the Area: Multiply the width by the height (Area = w × h).Calculation: 3 × 4 = 12 units².
   
2. Rotated Plots (Elite)
   In Elite mode, the sides are diagonal. You must use the Distance Formula between two adjacent vertices:\(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
   Calculate the distance from V1 to V2 (Length).
   Calculate the distance from V2 to V3 (Width).
   Multiply them and round to the nearest whole number.
   

Step 3: Input & Progress
Select your answer: Choose one of the four buttons at the bottom.
Instant Feedback: If you are correct, the area will turn cyan and be “verified.” If wrong, you’ll receive a calculation error.
Complete the Circuit: Each mission consists of 10 plots. Your accuracy is tracked in the top right corner.
Next Plot: After answering, click the “NEXT PLOT ➜” button to proceed.

The “Box” Method (Alternative)
If you find the distance formula difficult for rotated rectangles, you can use the Subtraction Method:
Draw a larger, grid-aligned rectangle (a “box”) that perfectly encloses the tilted rectangle.
Calculate the area of that large box.
Calculate the areas of the four right triangles created in the corners between the box and the tilted rectangle.
Subtract the area of those four triangles from the large box’s area.

The video gives a clear, step-by-step approach to learn how to find the area of a rectangle on the coordinate plane.

• Show Video

 

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