Lesson 5.45.4 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can find the area of a composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 5.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| Composite FigureSpanish: Figura compuesta | A shape made by putting two or more simple shapes together. | triangles joined together |
| DecomposeSpanish: Descomponer | To break a shape into smaller, simpler shapes. | hexagon → 6 triangles |
| AddSpanish: Sumar | Add up the areas of the smaller shapes to get the total. | T-shaped hallway: top rectangle = 30 sq ft, bottom rectangle = 28 sq ft → total = 30 + 28 = 58 sq ft |
| SubtractSpanish: Restar | Take away the area of a missing piece from a bigger shape. | A 14×10 pool with a 6×4 cutout: 140 − 24 = 116 sq ft of water surface |
| FormulaSpanish: Fórmula | A math rule written with symbols. | Rectangle: A = l × w; Triangle: A = ½ × b × h; use the right formula for each piece of a composite figure |
| Regular polygonSpanish: Polígono regular | A shape whose sides are all the same length and whose angles are all the same size. | stop sign, hexagon tile |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
Regular pentagon: sides 10 cm, apothem about 7 cm.
- 5 sides make 5 triangles.
- One triangle: ½ × 10 × 7 = 35 cm².
- Five triangles: 5 × 35 = 175.
Answer: Area ≈ 175 cm²
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
An L-shape is made of a 5 ft by 4 ft rectangle and a 3 ft by 2 ft rectangle. Find its area.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- I decomposed the figure into congruent .
- The area of one triangle is square units.
- There are triangles, so the total area is .
- I know the triangles are congruent because .
Word bank regular polygondecomposecongruenttrianglecenterbaseheightmultiplytotalareasquare unitscomposite figure
Watch out!A common mistake
A common mistake in Area of Composite Figures is adding every piece even when a piece has been cut out of the figure. For a 10 ft by 8 ft rectangle with a 3 ft by 2 ft rectangular notch cut from one corner, students compute the full rectangle 10 × 8 = 80 sq ft and stop, or they add the notch instead of removing it (80 + 6 = 86 sq ft) instead of subtracting it: 80 − (3 × 2) = 80 − 6 = 74 sq ft. Before submitting, check whether each piece is part of the figure (add it) or missing from the figure (subtract it).
Lesson 5.45.4 Small Group · Group 2
Group 2Challenge practice
Learning target I can find the area of a composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas, explain why the method works, and use it on a problem I have not seen before.
Why This Matters This is your challenge small group for Lesson 5.4. You can already get the answer — so in here the answer is the starting point. We ask when the method holds, when it breaks, and how you would convince someone who disagrees.
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1Complete each step, then write the final answer.
Two sides are missing. The dashed corner is outside the room. An L-shaped room has a bottom side of 12 m and a left side of 9 m. The top side is 5 m. The short right side is 4 m. Find the area.
- 1Find the two missing side lengths.
- 2Split into two rectangles and add. What is the area?
- 3Check: subtract the missing corner from the big rectangle.
Final answer: -
2Complete each step, then write the final answer.
The dashed triangle is cut out. A rectangular sign is 10 in by 6 in. A triangle is cut out of it. The triangle has a base of 4 in and a height of 3 in. Find the area of the sign that is left.
- 1Find the area of the whole rectangle.
- 2Find the triangle. Then find the area that is left.
- 3Why do we subtract the triangle and not add it?
Final answer: -
3Complete each step, then write the final answer.
A regular polygon splits into congruent triangles that meet at the center. Each triangle has a base of 5 cm and a height of 6 cm. The polygon’s area is 120 square centimeters. How many sides does it have?
Show your workFinal answer: -
4Complete each step, then write the final answer.
An L-shaped garden has a bottom side of 14 ft and a left side of 10 ft. The top side is 8 ft. The short right side is 6 ft. Find the area.
Show your workFinal answer: -
5Complete each step, then write the final answer.
A rectangular lawn is 25 m by 18 m. A flower bed inside it is a trapezoid with bases 4 m and 8 m and height 5 m. How many square meters of the lawn are grass?
Show your workFinal answer: -
6Complete each step, then write the final answer.
An L-shape fits in a 10 ft by 8 ft rectangle with a 4 ft by 4 ft corner missing. Ana adds two pieces and gets 58 square feet. Ben gets 64 square feet. What is the correct area?
Show your workFinal answer: