Perimeter of Composite Rectangles Game
One way to find the perimeter of any polygon is to add up the lengths of all its outer sides. There is a short-cut for L-shaped polygon. The perimeter of a L-shaped polygon is the same as the perimeter of its bounding box. Scroll down the page for a more detailed explanation.
 
This game generates a random L-shape polygon and require you to calculate the total perimeter. If you give a wrong answer, the game will give you the right answer.
 

How to Play the Perimeter of Composite Rectangles Game
In this game, you need to find the perimeter of a L-shape figure that consists of two non-overlapping rectangles. The game generates problems where you must find the perimeter of the shapes.
Here’s how to play:

1. Find the Perimeter: Find the missing dimensions and calculate the perimeter or use the shortcut for the L-shaped polygon.
   
2. Enter Your Answer: Type your answer for the total perimeter.
   
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 asked to try again.
   
4. New Shape: Click the Next Shape button (or press Enter again) for a new problem.
   Your score is tracked at the top, showing how many you’ve gotten right.
5. Restart Game Click “Restart Game” to restart the game.
    
   

How to Find the Perimeter of a Composite Rectangle
A composite rectangle is a shape made up of two or more simple rectangles joined together, often resulting in an L-shape or a U-shape.
Method 1: The Standard Approach (Adding All Sides
The most direct way to find the perimeter of any polygon is to add up the lengths of all its outer sides.
Steps:

1. Identify all sides: Count how many sides the shape has. A standard L-shape will have six sides.
   
2. Find the missing lengths: Composite rectangles often have two side lengths missing. You must deduce these missing lengths using the labeled dimensions.
   Horizontal Sides: If you know the total width and one inner horizontal segment, the missing segment is the total width minus the known segment.
   Missing W = Total W - Known W
   Vertical Sides: Similarly, if you know the total height and one inner vertical segment, the missing segment is the total height minus the known segment.
   Missing H = Total H - Known H
   
3. Calculate the Perimeter: Add the lengths of all six sides (four labeled and two calculated) together.
   Perimeter = Side1 + Side2 + Side3 + Side4 + Side5 + Side6
    
   

Method 2: The Rectangle Shortcut (Only works for L-shape)
For any shape that is a composite rectangle (a shape formed by removing a smaller rectangle from a corner of a larger one, or an L-shape), the perimeter can be found much more quickly.
The key insight is that even when the shape is cut, the Total Width and the Total Height of the shape remain the same as the original bounding box.
The Shortcut Rule:
The perimeter of an L-shaped composite rectangle is always equal to the perimeter of the smallest enclosing simple rectangle (the “bounding box”).
This is because the two inner segments you create (the two missing sides) simply replace the parts of the outer sides that were removed, but their combined lengths remain the same as the total width and total height.
Formula using the Shortcut:
If you know the Total Width (WT) and the Total Height (HT) of the L-shape, you can find the perimeter like this:
Perimeter = 2 × (Total Width + Total Height)
The shortcut allows you to skip finding the missing sides altogether, making it the preferred method for quick calculations!
 

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

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