Area of Regular Polygons

6.GR.1 · Unit 5 · Lesson 9

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 / TérminoDefinition / 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

  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?
    1. 15.6 sq ft
    2. 31.2 sq ft
    3. 11.2 sq ft
    4. 15.6 ft
  2. Problem 2
  3. Match each polygon to its total area.
  4. Find the Area Error
    1. Step 1: Decompose the hexagon — A regular hexagon = 6 triangles
    2. Step 2: Find area of one triangle — b = 5 m, h = 4.3 m
    3. Step 3: Calculate one triangle — A = ½ × 5 × 4.3 = 10.75 sq m
    4. Step 4: Find total area — Total = 10.75 + 6 = 16.75 sq m

    Which step has the mistake? Explain it and write the correct work.

Reflection / Reflexión

One thing I learned today / Una cosa que aprendí hoy: