Unit 5 · Standard 6.G.1
Area of Composite Figures
Key Vocabulary Level 1 support
Picture first, then the word, then a plain-language meaning. Say each word out loud.
An L-shaped room = a 12×8 rectangle joined to a 6×5 rectangle; total area = 96 + 30 = 126 sq ft
Composite Figure
A shape made by putting two or more simple shapes together.
Draw a dashed line across the L-shape to split it into two rectangles — now you can find each area separately
Decompose
To break a shape into smaller, simpler shapes.
T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft
Add
Add up the areas of the smaller shapes to get the total.
A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface
Subtract
Take away the area of a missing piece from a bigger shape.
Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure
Formula
A math rule written with symbols.
Key Ideas & Notes
- Your architecture firm is calculating the floor area of an L-shaped room for a client's new home.
- The contractor needs the total area to order the correct amount of flooring.
- The room can be split into two rectangles: one is 12 feet by 8 feet and the other is 6 feet by 5 feet.
- Break each composite figure into simpler shapes. Find the area of each part, then calculate the total area.
Think About It
- What does the shape of the room look like?
- Can you see simpler shapes inside the L-shape?
- What measurements are given for each part?
My Notes
Guided Examples
Example 1
An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?
Solution: Area 1 = 10 × 6 = 60 sq ft. Area 2 = 4 × 3 = 12 sq ft. Total = 60 + 12 = 72 sq ft.
Answer: A. 72 sq ft
Example 2
A rectangular patio is 15 ft × 10 ft with a 5 ft × 4 ft rectangular flower bed cut out. What is the remaining area?
Solution: Patio = 15 × 10 = 150 sq ft. Cutout = 5 × 4 = 20 sq ft. Remaining = 150 − 20 = 130 sq ft.
Answer: A. 130 sq ft
Example 3
Find the area of an L-shape made of a 5×3 rectangle and a 2×4 rectangle.
Solution: 5 × 3 = 15. 2 × 4 = 8. Total = 15 + 8 = 23 sq units.
Answer: A. 23 sq units
Write About the Math The Writing Revolution
I can explain my steps using the words composite figure, decompose, add, and subtract.
1. Kernel Sentence subject + verb
Model: Composite Figure is a shape made by putting two or more simple shapes together.Figura compuesta es una figura formada al juntar dos o más figuras simples.
Write a kernel sentence about composite figure. Use a subject and a verb.Escribe una oración base sobre figura compuesta. Usa un sujeto y un verbo.
2. Sentence Expansion because · but · so
Kernel: Composite Figure matters in mathFigura compuesta importa en matemáticas
Expand the kernel three ways. Add a reason, a contrast, and a result.
Composite Figure matters in math because ___.Figura compuesta importa en matemáticas porque ___.
Composite Figure matters in math, but ___.Figura compuesta importa en matemáticas, pero ___.
Composite Figure matters in math, so ___.Figura compuesta importa en matemáticas, entonces ___.
3. Sentence Types 4 ways to write a math idea
Tell one true fact about composite figure.Di un hecho verdadero sobre composite figure.
Composite figure ___.
Ask a question about composite figure.Haz una pregunta sobre composite figure.
How does ___ ?¿Cómo ___ ?
Show excitement about composite figure.Muestra entusiasmo sobre composite figure.
Wow, ___ !¡Guau, ___ !
Tell a partner what to do with composite figure.Dile a un compañero qué hacer con composite figure.
First, ___ .Primero, ___ .
4. Explain Your Reasoning use a sentence starter
I broke the figure into ___.Dividí la figura en ___.
I added the areas to get ___.Sumé las áreas para obtener ___.
This helps when ___.Esto ayuda cuando ___.
Try It
Solve on your own. Check the answer key when you are done.
1. Find the area of an L-shape made of a 5×3 rectangle and a 2×4 rectangle.
- 23 sq units
- 15 sq units
- 8 sq units
- 20 sq units
2. When should you subtract areas instead of adding them to find the area of a composite figure?
- When a piece is cut out or removed from a larger shape
- When the shapes overlap
- When one shape is larger than the other
- Always subtract — never add
Stretch Your Thinking Level 2 enrichment
Challenge task — explain your reasoning in full sentences.
A T-shaped room can be decomposed in two different ways. Show both ways and prove they give the same total area. Use a T-shape where the top is 14 ft × 4 ft and the stem is 6 ft × 10 ft.
Sentence starter: Way 1: I split it into ___ and ___. Areas: ___ + ___ = ___. Way 2: I used a ___ rectangle and subtracted ___. Areas: ___ − ___ = ___. Both give ___ sq ft.
Reflect — Exit Ticket
A composite figure is made of a 9 ft x 7 ft rectangle and a 3 ft x 4 ft rectangle joined together. What is the total area?
- 75 sq ft
- 63 sq ft
- 12 sq ft
- 75 ft
Answer Key & Teacher Guide
- Try It 1: A. 23 sq units — 5 × 3 = 15. 2 × 4 = 8. Total = 15 + 8 = 23 sq units.
- Try It 2: A. When a piece is cut out or removed from a larger shape — Subtract when a piece is removed from a larger shape (like a window cut from a wall). Add when two shapes are joined together (like an L-shape).
- Exit Ticket: A. 75 sq ft — Area 1 = 9 x 7 = 63 sq ft. Area 2 = 3 x 4 = 12 sq ft. Total = 63 + 12 = 75 square feet.
Writing (TWR) — what to look for
- Kernel sentence: A complete sentence needs a subject and a verb. Example: Composite Figure is a shape made by putting two or more simple shapes together.
- Expansion: because gives a reason, but shows a contrast or exception, so shows a result. Answers vary; each must keep the kernel idea and add the correct kind of detail.
- Sentence types: Statement ends with a period, question with "?", exclamation with "!", and a command starts with an action verb (a "bossy" verb).