The lesson
This lesson teaches Composite Figures. 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.
Area measures how much space a flat shape covers, in square units. Picture tiles on a floor. Each tile is one square unit.
Break complicated shapes into rectangles or triangles you already know how to measure, then add the pieces together.
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.
Area measures how much space a flat shape covers, in square units. Picture tiles on a floor. Each tile is one square unit.
Break complicated shapes into rectangles or triangles you already know how to measure, then add the pieces together.
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
Composite Figures shows up constantly in split unusual shapes into simple ones you already know. It also connects to what you will see on homework, quizzes, and the next unit in this grade.
Teachers often move fast in class. This page is here so you can pause, re-read, and practice until the idea feels familiar, not just until you have memorized a rule for one day.
Common mistakes to avoid
Rushing to the answer without writing steps. Middle-school math rewards clear work, and you catch errors earlier when steps are visible.
Mixing up similar ideas from the same topic. If two terms feel alike, make a two-column note: what is the same, what is different, and one example of each.
Key ideas from this lesson
- Break it into pieces
- When there's a hole
Video walkthrough
Area of Composite Shapes
Split a weird shape into rectangles and triangles.
Watch on YouTubeArea of a Composite Figure
Step-by-step practice with combined 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?