Calculate the Area of an L-Shaped Figure: 14×2 with 3×1 Extension

Composite Area with Rectangle Decomposition

What is the area of the shape below?

141414222111333

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Step-by-step video solution

Watch the teacher solve the problem with clear explanations
00:00 Calculate the area of the shape
00:03 Draw a parallel line to create 2 rectangles
00:06 Apply the formula to calculate the rectangle's area
00:09 Side(2) multiplied by side(4)
00:12 This is the area of rectangle 1
00:15 Apply the same formula to calculate rectangle 2's area
00:19 Side(1) x side(3)
00:22 This is the area of rectangle 2
00:25 Add up the areas to determine the total area of the shape
00:31 This is the solution

Step-by-step written solution

Follow each step carefully to understand the complete solution
1

Understand the problem

What is the area of the shape below?

141414222111333

2

Step-by-step solution

First, let's draw an imaginary line so that we get a shape containing one large rectangle and one small rectangle.

Then we can calculate the area of the large rectangle:

14×2=28 14\times2=28

Next we will calculate the area of the small rectangle:

1×3=3 1\times3=3

Finally, we combine the two areas to get the answer:
28+3=31 28+3=31

3

Final Answer

31 cm²

Key Points to Remember

Essential concepts to master this topic
  • Decomposition: Break L-shapes into simpler rectangles for easier calculation
  • Technique: Area of large rectangle: 14×2=28 14\times2=28 , small rectangle: 3×1=3 3\times1=3
  • Check: Total area should match sum of parts: 28+3=31 28+3=31 square units ✓

Common Mistakes

Avoid these frequent errors
  • Trying to use one formula for the entire L-shape
    Don't attempt to calculate the L-shape as a single rectangle = impossible measurement! L-shapes can't be measured with just length × width. Always break complex shapes into simple rectangles first, then add their areas.

Practice Quiz

Test your knowledge with interactive questions

Look at the rectangle ABCD below.

Side AB is 6 cm long and side BC is 4 cm long.

What is the area of the rectangle?
666444AAABBBCCCDDD

FAQ

Everything you need to know about this question

How do I know where to draw the dividing line?

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Look for places where you can create complete rectangles! In this L-shape, you can draw a vertical line to separate the main 14×2 rectangle from the 3×1 extension.

What if I break it up differently - will I get the same answer?

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Yes! You could also think of it as a large rectangle with a corner cut out. The total area will always be 31 square units regardless of how you decompose it.

Why can't I just multiply the longest sides together?

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Because L-shapes aren't rectangles! Using 14×3=42 counts some area twice and includes empty space. Always break into actual rectangles that exist in the shape.

How do I make sure I'm measuring the right dimensions?

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Follow each edge carefully and match dimensions that are directly across from each other. The main rectangle is 14 wide and 2 tall, while the extension is 3 wide and 1 tall.

What units should my final answer have?

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Since we're calculating area, use square units! If the measurements were in cm, your answer would be 31 cm². Always include the word 'square' or the ² symbol.

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