Lesson 5.45.4 · 5.9 Catch-Up
Start hereWords, worked example, and sentence starters
Learning target I can show I am caught up on Lessons 5.4 · 5.9 by using each lesson's big idea in mixed practice.
Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 5.4 · 5.9: 5.4 Apply Area Concepts to Solve Problems, 5.9 Area of Regular Polygons. Work one example from each lesson, then prove you're caught up in the mixed practice.
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 closed flat shape made of straight sides, where every side is the same length and every angle is 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.
A shape is made of a 6 ft by 2 ft rectangle joined to a 3 ft by 3 ft square. Find its total 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 Regular Polygons is stopping after finding the area of ONE triangle and reporting that as the total area
Lesson 5.45.4 · 5.9 Catch-Up
Catch-UpSkill bridge
Learning target I can show I am caught up on Lessons 5.4 · 5.9 by using each lesson's big idea in mixed practice.
Why This Matters Missed a lesson — or just want a refresher? This catch-up station reviews Lessons 5.4 · 5.9: 5.4 Apply Area Concepts to Solve Problems, 5.9 Area of Regular Polygons. Work one example from each lesson, then prove you're caught up in the mixed practice.
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1Complete each step, then write the final answer.
A shape is made of a 6 m by 3 m rectangle joined to a 2 m by 5 m rectangle. Find its total area.
Show your workHint Find each rectangle. They are joined, so add.
Final answer: -
2Complete each step, then write the final answer.
A rectangle is 8 ft by 5 ft. A 2 ft by 2 ft square is cut out of it. Find the area that is left.
Show your workHint The square is cut out, so subtract it.
Final answer: -
3Complete each step, then write the final answer.
A square splits into 4 equal triangles from its center. Each triangle has a base of 10 m and a height of 5 m. Find the area.
Show your workHint Find one triangle: half of base × height. Then multiply by 4.
Final answer: -
4Complete each step, then write the final answer.
A regular octagon splits into 8 equal triangles. Each triangle has a base of 2 in and a height of 2.4 in. Estimate the area.
Show your workHint Find one triangle. Then multiply by 8.
Final answer:
Explain your thinkingThe hexagon and the octagon both have triangles, but the totals are different. What two things decide the total area of a regular polygon?
Sentence starter The total area is ___ because one triangle is ___ and there are ___ triangles.