Apply Area Concepts to Solve Problems

6.GR.1 · Unit 5 · Lesson 4

Name   Period

Objectives / Objetivos

Content Objective: I can find the area of a composite figure by decomposing it into basic shapes, including a regular polygon split into triangles, and adding or subtracting the areas.

Language Objective: I can explain my steps using the words composite figure, decompose, add, and subtract.

Key Idea / Idea clave

Area of Composite Figures. 1. Decompose: Split the irregular shape into basic figures (rectangles, triangles, trapezoids). 2. Calculate: Find the area of each individual sub-figure. 3. Combine: Add the areas together (or subtract if a piece is removed/cut out)

I Notice / Observo

  • What does the shape of the room look like?
  • Can you see simpler shapes inside the L-shape?

I Wonder / Me pregunto

  • Is there more than one way to split this shape into rectangles?

Vocabulary / Vocabulario

Term / TérminoDefinition / Definición
Area of Composite Figures
Área de figuras compuestas		The total space inside a figure made of basic shapes. Formula: A = A₁ + A₂ — add the parts (or subtract a missing piece).
El espacio total dentro de una figura formada por figuras básicas. Fórmula: A = A₁ + A₂ — suma las partes (o resta la pieza que falta).
Composite Figure
Figura compuesta		A shape made by putting two or more simple shapes together.
Una figura formada al juntar dos o más figuras simples.
Decompose
Descomponer		To break a shape into smaller, simpler shapes.
Separar una figura en figuras más pequeñas y simples.
Add
Sumar		Add up the areas of the smaller shapes to get the total.
Sumar las áreas de las figuras pequeñas para obtener el total.
Subtract
Restar		Take away the area of a missing piece from a bigger shape.
Quitar el área de una parte que falta de una figura más grande.
Formula
Fórmula		A math rule written with symbols.
Una regla matemática escrita con símbolos.

Practice Preview / Vista previa de práctica

  1. An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?
    1. 72 sq ft
    2. 60 sq ft
    3. 12 sq ft
    4. 72 ft
  2. Problem 2
  3. Match each composite figure to its total area.
  4. Find the Area Error
    1. Step 1: Identify the shapes — Rectangle: 16 ft × 10 ft, with a 4 ft × 6 ft piece cut from the corner
    2. Step 2: Find the large rectangle area — A = 16 × 10 = 160 sq ft
    3. Step 3: Find the cutout area — A = 4 × 6 = 24 sq ft
    4. Step 4: Find total area — Total = 160 + 24 = 184 sq ft

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

Reflection / Reflexión

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