Apply Area Concepts to Solve Problems
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 / Término | Definition / 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
Read each task. Show your work in the spaces provided and explain how you know.
1. An L-shaped room is made of two rectangles: 10 ft × 6 ft and 4 ft × 3 ft. What is the total area?
- A 12 sq ft
- B 60 sq ft
- C 72 sq ft
- D 72 ft
Answer:
2.
Complete each empty cell. Show your reasoning below.
| Figure | Shape 1 Area | Shape 2 Area | Operation | Total Area |
|---|---|---|---|---|
| L-shaped deck | 48 sq ft | 20 sq ft | Add | |
| Floor with alcove | 90 sq ft | 15 sq ft | Add | |
| Wall with window cutout | 120 sq ft | 18 sq ft | Subtract | |
| Courtyard with fountain cutout | 200 sq ft | 36 sq ft | Subtract |
3. Match each composite figure to its total area.
Write the letter of the matching item in the blank.
| 1. | L-shape: 10×6 + 4×3 | A. | 130 sq ft | |
| 2. | T-shape: 14×4 + 6×10 | B. | 116 sq ft | |
| 3. | Wall 15×10 minus window 5×4 | C. | 110 sq ft | |
| 4. | Pool 14×10 minus cutout 6×5 | D. | 72 sq ft | |
| 5. | L-shape: 8×5 + 3×6 | E. | 58 sq ft | |
| 6. | Floor 12×8 minus vent 2×3 | F. | 90 sq ft |
4. Find the Area Error
Which step has the mistake, and what should it be?
Reflection / Reflexión
One thing I learned today / Una cosa que aprendí hoy: