How to Decompose Shapes into Rectangles to Find Area (Grade 6 Lesson)

📚 Decomposing Shapes into Rectangles: A 6th Grade Lesson

This lesson will guide you through the process of finding the area of irregular shapes by decomposing them into rectangles. We'll cover the objectives, materials needed, a warm-up activity, the main instruction, and an assessment to test your understanding.

🎯 Learning Objectives

• 📐 Understand the concept of area. Students will be able to define area as the amount of space inside a two-dimensional shape.
• ✂️ Decompose irregular shapes into rectangles. Students will be able to divide complex shapes into simpler rectangular components.
• ➕ Calculate the area of each rectangle. Students will be able to apply the formula for the area of a rectangle (length × width).
• 🧮 Find the total area by adding the areas of the rectangles. Students will be able to sum the areas of individual rectangles to find the total area of the original shape.

🛠️ Materials Needed

• 📏 Ruler or measuring tape: For measuring the sides of the shapes.
• ✏️ Pencil: For drawing lines to decompose shapes.
• 📄 Paper: For drawing and calculations.
• 🧱 Pre-drawn irregular shapes: Worksheets with various irregular shapes.
• 🖥️ Optional: Computer with geometry software: For visualizing and verifying results.

🔥 Warm-up (5 minutes)

Review: Area of a Rectangle

• 💭 Question 1: What is the formula for the area of a rectangle?

Answer: Area = length × width ( $A = l \times w$ )

• 🧱 Question 2: If a rectangle has a length of 5 cm and a width of 3 cm, what is its area?

Answer: $A = 5 \text{ cm} \times 3 \text{ cm} = 15 \text{ cm}^2$

📝 Main Instruction

Step-by-Step Guide

1. 👁️ Step 1: Look at the Irregular Shape: Observe the shape carefully. Identify if it can be easily divided into rectangles.
2. ✏️ Step 2: Divide the Shape: Use a pencil and ruler to draw lines that divide the irregular shape into rectangles. Make sure the lines are straight and create clear rectangular sections.
3. 📏 Step 3: Measure the Rectangles: Measure the length and width of each rectangle you've created. Record these measurements.
4. 🧮 Step 4: Calculate Individual Areas: Use the formula $A = l \times w$ to calculate the area of each rectangle.
5. ➕ Step 5: Add the Areas: Sum up the areas of all the rectangles to find the total area of the irregular shape.

Example:

Imagine an L-shaped figure. Divide it into two rectangles. Rectangle 1 has a length of 8 cm and a width of 3 cm. Rectangle 2 has a length of 5 cm and a width of 3 cm.

• ➕ Area of Rectangle 1: $A_1 = 8 \text{ cm} \times 3 \text{ cm} = 24 \text{ cm}^2$
• ➕ Area of Rectangle 2: $A_2 = 5 \text{ cm} \times 3 \text{ cm} = 15 \text{ cm}^2$
• 💡 Total Area: $A_{\text{total}} = A_1 + A_2 = 24 \text{ cm}^2 + 15 \text{ cm}^2 = 39 \text{ cm}^2$

✅ Assessment

Practice Quiz

Decompose each shape into rectangles and calculate the total area.

1. 📐 Question 1: A shape composed of two rectangles. Rectangle 1: length = 6 cm, width = 4 cm. Rectangle 2: length = 3 cm, width = 2 cm. What is the total area?

Answer: $A_1 = 6 \times 4 = 24 \text{ cm}^2$, $A_2 = 3 \times 2 = 6 \text{ cm}^2$, $A_{\text{total}} = 24 + 6 = 30 \text{ cm}^2$

2. 📐 Question 2: A shape composed of two rectangles. Rectangle 1: length = 7 m, width = 2 m. Rectangle 2: length = 4 m, width = 3 m. What is the total area?

Answer: $A_1 = 7 \times 2 = 14 \text{ m}^2$, $A_2 = 4 \times 3 = 12 \text{ m}^2$, $A_{\text{total}} = 14 + 12 = 26 \text{ m}^2$

3. 📐 Question 3: A shape composed of two rectangles. Rectangle 1: length = 9 in, width = 1 in. Rectangle 2: length = 5 in, width = 2 in. What is the total area?

Answer: $A_1 = 9 \times 1 = 9 \text{ in}^2$, $A_2 = 5 \times 2 = 10 \text{ in}^2$, $A_{\text{total}} = 9 + 10 = 19 \text{ in}^2$

4. 📐 Question 4: A shape composed of two rectangles. Rectangle 1: length = 10 ft, width = 3 ft. Rectangle 2: length = 2 ft, width = 2 ft. What is the total area?

Answer: $A_1 = 10 \times 3 = 30 \text{ ft}^2$, $A_2 = 2 \times 2 = 4 \text{ ft}^2$, $A_{\text{total}} = 30 + 4 = 34 \text{ ft}^2$

5. 📐 Question 5: A shape composed of two rectangles. Rectangle 1: length = 11 cm, width = 5 cm. Rectangle 2: length = 3 cm, width = 3 cm. What is the total area?

Answer: $A_1 = 11 \times 5 = 55 \text{ cm}^2$, $A_2 = 3 \times 3 = 9 \text{ cm}^2$, $A_{\text{total}} = 55 + 9 = 64 \text{ cm}^2$

6. 📐 Question 6: A shape composed of two rectangles. Rectangle 1: length = 12 m, width = 4 m. Rectangle 2: length = 6 m, width = 1 m. What is the total area?

Answer: $A_1 = 12 \times 4 = 48 \text{ m}^2$, $A_2 = 6 \times 1 = 6 \text{ m}^2$, $A_{\text{total}} = 48 + 6 = 54 \text{ m}^2$

7. 📐 Question 7: A shape composed of two rectangles. Rectangle 1: length = 13 in, width = 2 in. Rectangle 2: length = 4 in, width = 4 in. What is the total area?

Answer: $A_1 = 13 \times 2 = 26 \text{ in}^2$, $A_2 = 4 \times 4 = 16 \text{ in}^2$, $A_{\text{total}} = 26 + 16 = 42 \text{ in}^2$