Lesson 5.95.9 Small Group · Group 2
Start hereWords, worked example, and sentence starters
Learning target I can find the area of a regular polygon by decomposing it into triangles, explain why the method works, and use it on a problem I have not seen before.
Start hereWords for this lesson
Read each word before you begin. Say it out loud.
| Word | What it means | Example |
|---|---|---|
| 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. | A stop sign is a regular octagon — all 8 sides are the same length and all 8 angles are equal |
| DecomposeSpanish: Descomponer | To break a shape into smaller, simpler shapes. | Draw lines from the center of a hexagon to each corner → you get 6 equal triangles you can find the area of |
| TriangleSpanish: Triángulo | A shape with three sides. | Each triangle inside a decomposed hexagon has a base = one side of the hexagon and height = distance from center to side |
| CompositeSpanish: Compuesto | Made by putting two or more simple shapes together. | 6 triangles, each with area 15 sq ft, combine to form a hexagon with total area = 6 × 15 = 90 sq ft |
| FormulaSpanish: Fórmula | A math rule written with symbols. | For a regular hexagon: Total Area = 6 × (½ × b × h), where b = side length and h = height of each triangle |
How it worksWorked example
These numbers are not on your problems. The steps are. Follow them with your own numbers.
A regular hexagon has sides of 10 inches. Its area is about 261 square inches. Find the height of each center triangle.
- Find the area of one triangle: 261 ÷ 6 = 43.5
- Double it to undo the half: 43.5 × 2 = 87
- Divide by the base: 87 ÷ 10 = 8.7
- Check with the area: 6 × (1/2 × 10 × 8.7) = 261
- Each center triangle has a height of about 8.7 inches.
Now you trySame steps, your turn
The steps are the same as the worked example. The numbers are yours. Do the work.
A regular pentagon splits into 5 equal triangles. Each triangle has a base of 4 cm and a height of 3 cm. The height is rounded, so estimate the area.
Say it and write itSentence starters
Finish each sentence out loud with a partner. Then use them in your writing.
- The total area is because one triangle is and there are triangles.
Word bank Regular PolygonDecomposeTriangleCompositeFormulatrianglehalfbaseheightmultiplytotalnumber of sides
Watch outA 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 — or adding the number of triangles instead of multiplying. Remember: total area = (one triangle's area) × (number of sides), not (one triangle's area) + (number of sides).
Lesson 5.95.9 Small Group · Group 2
Group 2Challenge practice
Learning target I can find the area of a regular polygon by decomposing it into triangles, explain why the method works, and use it on a problem I have not seen before.
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1Complete each step, then write the final answer.
The pentagon is 5 equal triangles. A regular pentagon has sides of 10 cm. Its area is about 172.5 square centimeters. Find the height of each center triangle.
- 1What is the area of one center triangle?
- 2Double it to undo the half. What is base × height?
- 3Divide by the base. What is the height?
Final answer: -
2Complete each step, then write the final answer.
A regular hexagon has an area of about 374.4 square feet. Each center triangle has a height of 10.4 ft. How long is each side?
- 1What is the area of one center triangle?
- 2Double it. What is base × height?
- 3Divide by the height. How long is each side?
- 4Why do we double before we divide by the height?
Final answer: -
3Complete each step, then write the final answer.
A regular heptagon has 7 sides of 4 m. Each center triangle has a height of 4.2 m. Estimate its area.
Show your workFinal answer: -
4Complete each step, then write the final answer.
A regular polygon is made of equal center triangles. Each triangle has a base of 6 in and a height of 7.2 in. The area is about 172.8 square inches. How many sides does it have?
Show your workFinal answer: -
5Complete each step, then write the final answer.
A window is a regular decagon with sides of 4 in. Its area is about 124 square inches. What is the height of each center triangle?
Show your workFinal answer: -
6Complete each step, then write the final answer.
A regular hexagon has sides of 14 cm. Each center triangle has a height of 12.1 cm. Ana finds perimeter × height ÷ 2. Ben finds one triangle and multiplies by 6. What area do they get?
Show your workFinal answer: