Worked example 1
An “L” shape has a 10 × 6 rectangle on top and a 4 × 3 rectangle attached below. Find the total area.
Start by writing the calculation clearly: A₁ = 10 × 6 = 60. A₂ = 4 × 3 = 12. Total: 60 + 12 = 72 sq units.
Answer: 72 sq units
Grade 6 Math · Topic 56
Area of Composite Figures
A composite figure is built from two or more basic shapes (rectangles, triangles, trapezoids). To find its area, decompose it into pieces you know, find each piece's area, and add them up. Sometimes it's easier to find a big shape's area and subtract the missing piece.
Lesson alignment: 6.G.A.1 · Take your time. You can return to this lesson whenever you need it.
Explore visually
Break a composite figure into rectangles
Split the L-shape into two non-overlapping rectangles, or subtract the missing corner from the outside rectangle.
Think first: Would you split the shape into rectangles or subtract the missing corner?
Ready? Reveal the model and try your prediction
Swipe horizontally to see the full diagram.
Turn on JavaScript to adjust this model. The examples and practice below work without it.
Follow the worked examples
Read each step, then cover the explanation and see if you can explain why it works.
Worked example 2
A 12 × 8 rectangle has a 4 × 3 rectangle cut out of one corner. Find the remaining area.
Big: 12 × 8 = 96. Cutout: 4 × 3 = 12. Remaining: 96 - 12 = 84 sq units.
Answer: 84 sq units
Try a few on your own
Work these on paper first. Open “Check” when you are ready to compare your answer.
- Rect 5 × 4 + Rect 3 × 2
Check
26
- Rect 8 × 6 + Tri b=4, h=6
Check
60
- Rect 10 × 5 - Rect 4 × 2
Check
42
- Rect 12 × 8 - Tri b=6, h=4
Check
84
- Sq 6 + Rect 6 × 3
Check
54
- Trap b₁=5, b₂=9, h=4 + Sq 4
Check
44
- Rect 14 × 9 - Sq 5
Check
101
- Rect 15 × 10 - Tri b=6, h=10
Check
120
Try this situation 1
A room is shaped like a rectangle 20 × 12 ft with a 4 × 4 ft closet sticking out. Find the total floor area.
Show a worked solution
Answer: 256 ft².
Start by writing the calculation clearly: 20 × 12 = 240. Closet 4 × 4 = 16. Total 240 + 16 = 256.
Try this situation 2
A garden is a 30 × 20 ft rectangle with a square fountain (6 ft on a side) in it. How much area is for plants?
Show a worked solution
Answer: 564 ft².
Garden 600. Fountain 36. Plants: 600 - 36 = 564.
Fresh questions · saved on this device
Practice this skill
Try a fresh set each time. Answer one question, check your thinking, and read the explanation. If you miss one, return to the visual model and try another round.
Question 1 of 50 correct so far
Session complete
Check what you learned
Answer these five questions on your own. You can review the explanations after you submit and try again whenever you like. This short check is for practice, not a grade.
Practice and finish
Try the linked topic quiz for more practice. If something is tricky, return to the example and look for the step that changes the numbers or representation.
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More Grade 6 resources
Use these free materials if you want another explanation, extra paper practice, or a broader review.