Family Math Studio Grade 6 Math · Neft Teacher

Family Math Studio · Lesson guide Guía de la lección

Unit 5, Lesson 9: Area of Regular Polygons

Standard 6.GR.1

What students are learning Qué aprenden

Key idea: A regular polygon has equal sides. Split it from the middle into matching triangles. Find the area of one triangle, then multiply by how many triangles there are. A hexagon made of 6 triangles of 12 square cm each has area 6 × 12 = 72 square cm.Idea clave: Un polígono regular tiene lados iguales. Divídelo desde el centro en triángulos iguales. Halla el área de un triángulo y multiplícala por el número de triángulos. Un hexágono formado por 6 triángulos de 12 centímetros cuadrados cada uno tiene un área de 6 × 12 = 72 centímetros cuadrados.

Words to know Palabras clave

Area of Regular Polygons Área de polígonos regulares
Split it into equal triangles, then add their areas.
Divídelo en triángulos iguales y suma sus áreas.
Regular Polygon Polígono regular
A closed shape with equal sides and equal angles.
Una figura cerrada con lados iguales y ángulos iguales.
Decompose Descomponer
Break a number or shape into smaller parts.
Separar un número o una figura en partes más pequeñas.
Triangle Triángulo
A shape with three sides.
Una figura de tres lados.
Composite Compuesto
Made of two or more simple shapes.
Formado por dos o más figuras simples.
Formula Fórmula
A rule written with letters and numbers.
Una regla escrita con letras y números.

Sentence starters Frases para empezar

I know ___ because ___.

First, I ___. Then, I ___.

The answer is ___, so ___.

How we did it in class today Cómo lo hicimos hoy en clase

  1. My hexagon has 6 equal sides. Each side is 6 feet, and each center triangle has a height of 5.2 feet. Use the rounded height to estimate the area.
  2. First I find one triangle: A = ½ × base × height = ½ × 6 × 5.2.
  3. I multiply: 6 × 5.2 = 31.2, then ½ × 31.2 = 15.6 square feet.
  4. A hexagon has 6 sides, so it has 6 equal triangles.
  5. I multiply: 6 × 15.6 = 93.6. So the total area is 93.6 square feet.

Play with today's math Jueguen con las matemáticas

Interactive Lesson Model — This is the exact same interactive tool your student used in class today. Change the numbers and watch what happens!

Modelo interactivo de la lección — Esta es la misma herramienta interactiva que su estudiante usó en clase hoy. ¡Cambie los números y observe qué sucede!

Works on a phone, a tablet, or a computer. Nothing to install, nothing to sign in to.

Try this together Inténtenlo juntos

Pick one question to talk about. You don't need to do them all!

Match each polygon to its total area. Use the given heights; nonsquare heights are rounded, so their areas are estimates.

Hexagon: 6 triangles, each ½×6×5.2

Check the answer

The answer is: 93.6 sq ft

Take-home sheet Hoja para llevar a casa

Lesson 5.9: Print the sheet (PDF) · Answers and talk notes (PDF) · Edit it (Word)

Lección 5.9: Imprimir la hoja (PDF) · Respuestas y notas para conversar (PDF) · Editarla (Word)

If they get stuck... Si se traban...

Watch out for this: 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).

Try asking: "Can you show me how you got that? Did we miss a step?"
Pregunte: «¿Puedes mostrarme cómo lo hiciste? ¿Nos saltamos algún paso?» Hablar de las matemáticas en voz alta ayuda mucho.

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