Area of Regular Polygons
Name Period
Objectives / Objetivos
Content Objective: I can find the area of a regular polygon by decomposing it into triangles.
Language Objective: I can explain my steps using the words regular polygon, decompose, triangle, and composite.
Key Idea / Idea clave
Area of Regular Polygons. Formula: Area = (Number of Sides) × (Area of One Triangle). 1. Decompose the regular polygon from center into n congruent triangles. 2. Find the area of one triangle using A = ½ × side × apothem (height). 3. Multiply by the total number of sides
I Notice / Observo
- What shape is the skylight?
- How many sides does a hexagon have?
I Wonder / Me pregunto
- How can we break a hexagon into shapes whose area we already know?
Vocabulary / Vocabulario
| Term / Término | Definition / Definición |
|---|---|
| Area of Regular Polygons Área de polígonos regulares | The space a regular polygon covers. Split it from the center into identical triangles, find one triangle's area, then multiply by how many there are. El espacio que cubre un polígono regular. Divídelo desde el centro en triángulos idénticos, halla el área de uno y multiplícala por cuántos hay. |
| Regular Polygon Polígono regular | A closed flat shape made of straight sides, where every side is the same length and every angle is the same size. Una figura plana cerrada de lados rectos, donde todos los lados miden lo mismo y todos los ángulos son iguales. |
| Decompose Descomponer | To break a shape into smaller, simpler shapes. Separar una figura en figuras más pequeñas y simples. |
| Triangle Triángulo | A shape with three sides. Una figura de tres lados. |
| Composite Compuesto | Made by putting two or more simple shapes together. Formada al juntar dos o más figuras simples. |
| Formula Fórmula | A math rule written with symbols. Una regla matemática escrita con símbolos. |
Practice Preview / Vista previa de práctica
Read each task. Show your work in the spaces provided and explain how you know.
1. A regular hexagon is divided into 6 equal triangles from the center. Each triangle has a base of 6 ft and a height of 5.2 ft. What is the area of one triangle? Use the given heights; nonsquare heights are rounded, so their areas are estimates.
- A 11.2 sq ft
- B 15.6 sq ft
- C 15.6 ft
- D 31.2 sq ft
Answer:
2. Complete the table: find one central triangle’s area and the polygon’s total area. Use the given rounded heights for estimates; the square dimensions are exact.
Complete each empty cell. Show your reasoning below.
| Polygon | Number of Triangles | Triangle Base | Triangle Height | Area of One Triangle | Total Area |
|---|---|---|---|---|---|
| Hexagon | 6 | 6 ft | 5.2 ft | ||
| Pentagon | 5 | 8 ft | 5.5 ft | ||
| Square | 4 | 5 ft | 2.5 ft | ||
| Octagon | 8 | 4 ft | 4.8 ft |
3. Match each polygon to its total area. Use the given heights; nonsquare heights are rounded, so their areas are estimates.
Write the letter of the matching item in the blank.
| 1. | Hexagon: 6 triangles, each ½×6×5.2 | A. | 69 sq ft | |
| 2. | Pentagon: 5 triangles, each ½×8×5.5 | B. | 110 sq ft | |
| 3. | Octagon: 8 triangles, each ½×4×4.8 | C. | 76.8 sq ft | |
| 4. | Square: 4 triangles, each ½×5×2.5 | D. | 25 sq ft | |
| 5. | Decagon: 10 triangles, each about ½×3×4.6 | E. | 93.6 sq ft | |
| 6. | Equilateral triangle: 3 central triangles, each about ½×4×1.2 | F. | 7.2 sq ft |
4. Find the Area Error (use rounded heights)
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: