Area of Composite Rectangles Game (U-Shaped)
To find the total area of a U-shped composite, we can use the Subtraction Method or Decomposition Method. You can use either the Decomposition Method (splitting it into three smaller rectangles) or the Subtraction Method (calculating the area of the large outer rectangle and subtracting the empty inner space). Scroll down the page for a more detailed explanation.
 
This game generates a U-shaped composite figure and asks you to calculate its total area. If you give a wrong answer, the game will give you the right answer.
 
Area of Composite Rectangles (L-Shape)
Area of Composite Rectangles (U-Shape)
 

U-Shape Area Challenge

Find the total area of the U-shaped figure below. Assume all angles are $90^\circ$.

Score:

0 / 0

Area = Check Area

Next Problem Restart Game

 

How to Play the Area of Composite Rectangles Game (U-Shaped)
In this game, you need to find the area of a U-shape figure that consists of two non-overlapping rectangles. The game generates problems where you must find the area of the composite shapes.
Here’s how to play:

1. Find the Area: Find the missing dimensions and calculate the area.
   
2. Enter Your Answer: Type your answer for the total area.
   
3. Check Your Work: Click the Check button (or press the Enter key). The game will tell you if you’re correct. If you are wrong, you will be shown the correct answer.
   
4. Get a New Problem: Click the Next Problem button (or press Enter again) for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right out of the total you’ve tried.
5. Restart Game Click “Restart Game” to restart the game.
    
   

The Area of Composite Rectangles (U-Shaped)
Here is a step-by-step guide on the two main methods for calculating their area.
Method 1: Subtraction (The Box Method)
This method involves imagining the shape as a large, complete rectangle with a piece cut out of it.
Steps:

1. Form a Large Rectangle: Imagine a larger, complete rectangle that completely encloses the composite figure. You are essentially “filling in” the missing rectangular piece.
   
2. Determine Overall Dimensions: Find the total length and total width of this imaginary large rectangle.
   
3. Calculate the Total Area: Calculate the area of this large, imaginary rectangle.
   
4. Calculate the Missing Area: Determine the length and width of the small rectangular piece that you mentally “filled in” (the cutout section). Calculate the area of this missing piece.
   
5. Subtract to Find the Composite Area: Subtract the area of the missing (cutout) piece from the total area of the large rectangle.
    
   Method 2: Decomposition (Breaking It Apart)
   Steps:
   
6. Decompose the Figure: Draw one or more straight lines to divide the composite shape into simple, separate rectangles. For an L-shaped figure, you typically draw one line to form two rectangles.
   
7. Determine Missing Dimensions: Use the dimensions provided on the original figure to find the lengths and widths of your new, smaller rectangles.
   Example: If the total width is 10 and the bottom segment of the L-shape is 4, the top segment’s width must be 10 - 4 = 6.
   
8. Calculate Individual Areas: Use the standard area formula (Area = length × width) for each small rectangle you created.
   
9. Find the Total Area: Add the areas of all the smaller rectangles together.
    
   

The video gives a clear, step-by-step approach to find the area of a composite figure.

• Show Video

 

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