How do you find the area of an L-shaped figure? The easiest method is to split the shape into two simple rectangles, find each rectangle’s area, and add the results together. In the video, the total area is 38 m².
L-shaped figures appear often in geometry, worksheets, home-improvement measurements, floor plans, and real-world design problems. Although the shape is not a single rectangle, it can be divided into rectangles whose areas are easy to calculate.
The Quick Answer: 38 m²
The L-shaped figure can be divided into two rectangles:
Rectangle A has an area of 14 m², and rectangle B has an area of 24 m²:
Understand the Shape
The overall shape has these important measurements:
| Measurement | Value | Meaning |
|---|---|---|
| Overall height | 7 m | Height of the left section |
| Top width | 2 m | Width of rectangle A |
| Overall length | 10 m | Length along the bottom |
| Right-side height | 3 m | Height of rectangle B |
Step 1: Find the Area of Rectangle A
Rectangle A is the tall section on the left. Its length is 7 m and its width is 2 m.
So, the area of the left rectangle is 14 square meters.
Step 2: Find the Area of Rectangle B
Rectangle B is the horizontal section along the bottom. Its height is 3 m. To find its length, subtract the 2 m width of rectangle A from the total length of 10 m:
Now multiply the length and width of rectangle B:
So, the area of the bottom rectangle is 24 square meters.
Step 3: Add the Two Rectangle Areas
The complete L-shaped figure is made from rectangles A and B. Add their areas:
Therefore, the area of the L-shaped figure is:
The Formula Behind the Trick
For an L-shaped figure divided into two non-overlapping rectangles, use:
For the measurements in the video:
An Alternative Method: Subtract the Missing Corner
You can also imagine the L-shape inside a large 10 m × 7 m rectangle. Then subtract the missing top-right corner.
The missing corner has a width of 10 − 2 = 8 m and a height of 7 − 3 = 4 m:
Both methods give the same result. Splitting the shape into two rectangles is often easier for beginners, while subtracting the missing corner is a useful alternative for more advanced problems.
Common Mistakes to Avoid
Do not use 10 m as the length of rectangle B. The bottom rectangle begins after the 2 m-wide left section, so its length is 10 − 2 = 8 m.
Do not multiply the total height of 7 m by the full bottom length of 10 m unless you are calculating the area of the enclosing rectangle. The L-shape does not cover the missing top-right corner.
Always label your units as square meters, written as m². Area measures the amount of surface inside a shape, so the unit is squared.
Practice Problems
Try these composite-area problems by splitting each shape into rectangles:
- A shape has rectangle areas of 12 m² and 20 m². What is the total area?
- An L-shaped figure has a tall rectangle measuring 6 m × 3 m and a bottom rectangle measuring 8 m × 2 m. What is the total area?
- A floor plan is split into rectangles measuring 5 ft × 4 ft and 9 ft × 3 ft. What is the total area?
Answer Key
- 12 + 20 = 32 m²
- (6 × 3) + (8 × 2) = 18 + 16 = 34 m²
- (5 × 4) + (9 × 3) = 20 + 27 = 47 ft²
Final Takeaway
To find the area of an L-shaped figure, divide it into two non-overlapping rectangles. Calculate each rectangle’s area using length × width, then add the results:
This method works for geometry homework, composite figures, floor-plan measurements, and many real-world area problems.
Frequently Asked Questions
What is the area of the L-shaped figure in the video?
The area is 38 m².
Why is rectangle B’s length 8 m?
The total bottom length is 10 m, but the left rectangle already uses 2 m. Therefore, the remaining length is 10 − 2 = 8 m.
What formula is used to find the area of a rectangle?
The formula is Area = length × width.
Can I solve an L-shape by subtracting a rectangle?
Yes. Find the area of the large enclosing rectangle, find the area of the missing corner, and subtract the missing area from the large area.
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