Learn on PengiBig Ideas Math, Course 2Chapter 8: Circles and Area

Lesson 4: Areas of Composite Figures

In this Grade 7 lesson from Big Ideas Math, Course 2 (Chapter 8: Circles and Area), students learn how to find the area of composite figures by decomposing them into familiar shapes such as rectangles, triangles, parallelograms, and semicircles. Students apply area formulas for each component and sum the results to find the total area. The lesson includes real-life applications like calculating the area of a portion of a basketball court.

Section 1

Methods for calculating area of composite figures

Property

There are several methods for calculating the area of composite figures:

  1. Count the unit squares enclosed, including estimates from partial squares.
  2. Use multiplication for rectangles (Area=length×widthArea = length \times width).
  3. Break the composite figure into simpler shapes (rectangles, triangles, circles) and add their areas together.

Examples

Section 2

Grid-Based Area Counting for Composite Figures

Property

To find the area of a composite figure on a grid, count whole squares as 11 square unit each, partial squares as 12\frac{1}{2} square unit each (or estimate fractional parts), then sum:

Total Area=whole squares+partial squares\text{Total Area} = \text{whole squares} + \text{partial squares}

Examples

Section 3

Method 1: Decomposition (The Addition Method)

Property

Decomposition means breaking an irregular figure into smaller, non-overlapping shapes that you already know.
Total Area = Area of Shape 1 + Area of Shape 2 + ...

Examples

  • L-Shape: An L-shaped room can be split into two rectangles. If one rectangle measures 12 by 4 units (Area = 48) and the other is 2 by 6 units (Area = 12), the total area is 48 + 12 = 60 square units.
  • House Shape: A shape looks like a house. It is formed by a rectangle (8 by 4 units, Area = 32) with a triangle on top (base 8, height 3, Area = 12). The total area is 32 + 12 = 44 square units.

Explanation

Think of this method like building with LEGOs! You break down a strangely shaped room or garden into simple blocks like rectangles and triangles. Calculate the area of each individual block, and then simply add them all together to get the total area.

Lesson overview

Expand to review the lesson summary and core properties.

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Section 1

Methods for calculating area of composite figures

Property

There are several methods for calculating the area of composite figures:

  1. Count the unit squares enclosed, including estimates from partial squares.
  2. Use multiplication for rectangles (Area=length×widthArea = length \times width).
  3. Break the composite figure into simpler shapes (rectangles, triangles, circles) and add their areas together.

Examples

Section 2

Grid-Based Area Counting for Composite Figures

Property

To find the area of a composite figure on a grid, count whole squares as 11 square unit each, partial squares as 12\frac{1}{2} square unit each (or estimate fractional parts), then sum:

Total Area=whole squares+partial squares\text{Total Area} = \text{whole squares} + \text{partial squares}

Examples

Section 3

Method 1: Decomposition (The Addition Method)

Property

Decomposition means breaking an irregular figure into smaller, non-overlapping shapes that you already know.
Total Area = Area of Shape 1 + Area of Shape 2 + ...

Examples

  • L-Shape: An L-shaped room can be split into two rectangles. If one rectangle measures 12 by 4 units (Area = 48) and the other is 2 by 6 units (Area = 12), the total area is 48 + 12 = 60 square units.
  • House Shape: A shape looks like a house. It is formed by a rectangle (8 by 4 units, Area = 32) with a triangle on top (base 8, height 3, Area = 12). The total area is 32 + 12 = 44 square units.

Explanation

Think of this method like building with LEGOs! You break down a strangely shaped room or garden into simple blocks like rectangles and triangles. Calculate the area of each individual block, and then simply add them all together to get the total area.