The lesson
Read each section in order, work through every example on paper, then use the practice problems and quick check at the bottom.
Break it into pieces
A composite figure is made of simpler shapes joined together. Split it into rectangles and triangles, find each area, then add them up.
When there's a hole
If a shape has a piece cut out (like a picture frame), find the outer area and subtract the inner area.
An L-shape is an 8 × 6 rectangle with a 3 × 2 corner cut out. Find the area.
- 1Whole rectangle: 8 × 6 = 48.
- 2Cut-out corner: 3 × 2 = 6.
- 348 − 6 = 42 square units.
Why this matters
Split unusual shapes into simple ones you already know.
These ideas show up on homework, quizzes, and the next unit in this grade. Getting comfortable here saves time later when the problems stack more steps together.
Common mistakes to avoid
Rushing to the answer without writing steps. Clear work helps you catch mistakes and shows your reasoning.
Re-reading the question too quickly. Underline what you are solving for before you start calculating.
Key ideas from this lesson
- Break it into pieces
- When there's a hole
Video walkthroughs
Area of Composite Shapes
Split a weird shape into rectangles and triangles.
Watch on YouTube
Area of a Composite Figure
Step-by-step practice with combined shapes.
Watch on YouTube
Area of Triangles Intuition
Add triangle areas when decomposing composite shapes.
Watch on YouTubePractice
For each problem: write your work in the box, type your answer, and check it. If you are stuck, reveal the solution one step at a time. Do not skip straight to the final answer.
Exercise 1
Try it yourselfAn L-shape is a 10 × 6 rectangle with a 4 × 3 corner removed. Find the area.
Step-by-step solution
- 1Whole rectangle: 10 × 6 = 60.
- 2Cut-out: 4 × 3 = 12.
- 360 − 12 = 48 square units.
Exercise 2
Try it yourselfA figure is made of a 5 × 8 rectangle topped by a triangle with base 5 and height 3. Find the total area.
Step-by-step solution
- 1Rectangle: 5 × 8 = 40.
- 2Triangle: ½ × 5 × 3 = 7.5.
- 3Total: 40 + 7.5 = 47.5 square units.
Exercise 3
Try it yourselfA 12 × 9 poster has a 6 × 4 rectangular hole cut in the center. Find the remaining area.
Step-by-step solution
- 1Outer area: 12 × 9 = 108.
- 2Hole: 6 × 4 = 24.
- 3108 − 24 = 84 square units.
Exercise 4
Try it yourselfSplit a T-shape into two rectangles: top 8 × 2 and stem 3 × 6. Find the total area.
Step-by-step solution
- 1Top: 8 × 2 = 16.
- 2Stem: 3 × 6 = 18.
- 316 + 18 = 34 square units.
Exercise 5
Try it yourselfA room is 15 ft by 12 ft with a 5 ft by 4 ft closet cut out. How much floor area needs carpet?
Step-by-step solution
- 1Full floor: 15 × 12 = 180 ft².
- 2Closet: 5 × 4 = 20 ft².
- 3Carpet area: 180 − 20 = 160 ft².
Quick check
Answer all questions. Retake the quiz until you feel confident before moving on.
Composite Figures
Question 1 of 4
An L-shape is an 8 × 6 rectangle with a 3 × 2 corner removed. What is its area?