Area of Regular Polygons

6.GR.1 · Unit 5 · Lesson 4

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

A regular polygon splits into the same number of triangles as it has sides, so total area = (one triangle's area) × (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
Regular Polygon
Polígono regular		A shape where all sides and all angles are equal.
Una figura donde todos los lados y 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: