Learn on PengiBig Ideas Math, Advanced 2Chapter 13: Circles and Area

Section 13.4: Areas of Composite Figures

In this Grade 7 lesson from Big Ideas Math Advanced 2, students learn how to find the area of composite figures by decomposing them into familiar shapes such as rectangles, triangles, semicircles, and parallelograms. Students apply area formulas for each component and sum the results to find the total area. The lesson is part of Chapter 13: Circles and Area and includes real-life applications such as calculating the area of a basketball court section.

Section 1

Methods for calculating area of composite figures

Property

There are several methods for calculating the area of a composite figure:

  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

Area of Rectangles

Property

  • Rectangles have four sides and four right (90∘90^\circ) angles.
  • The lengths of opposite sides are equal.
  • The area, AA, of a rectangle is the length times the width.
A=L⋅WA = L \cdot W

Examples

Section 3

Area of Triangles

Property

The area of a triangle is one-half the base, bb, times the height, hh.

A=12bhA = \frac{1}{2}bh

Examples

Section 4

Area of Semicircles

Property

The area of a semicircle is half the area of a full circle:

A=πr22A = \frac{\pi r^2}{2}

where rr is the radius of the semicircle.

Book overview

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Chapter 13: Circles and Area

  1. Lesson 1

    Section 13.1: Circles and Circumference

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  2. Lesson 2

    Section 13.2: Perimeters of Composite Figures

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  3. Lesson 3

    Section 13.3: Areas of Circles

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  4. Lesson 4Current

    Section 13.4: Areas of Composite Figures

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Section 1

Methods for calculating area of composite figures

Property

There are several methods for calculating the area of a composite figure:

  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

Area of Rectangles

Property

  • Rectangles have four sides and four right (90∘90^\circ) angles.
  • The lengths of opposite sides are equal.
  • The area, AA, of a rectangle is the length times the width.
A=L⋅WA = L \cdot W

Examples

Section 3

Area of Triangles

Property

The area of a triangle is one-half the base, bb, times the height, hh.

A=12bhA = \frac{1}{2}bh

Examples

Section 4

Area of Semicircles

Property

The area of a semicircle is half the area of a full circle:

A=πr22A = \frac{\pi r^2}{2}

where rr is the radius of the semicircle.

Book overview

Jump across lessons in the current chapter without opening the full course modal.

Continue this chapter

Chapter 13: Circles and Area

  1. Lesson 1

    Section 13.1: Circles and Circumference

    LearnPractice
  2. Lesson 2

    Section 13.2: Perimeters of Composite Figures

    LearnPractice
  3. Lesson 3

    Section 13.3: Areas of Circles

    LearnPractice
  4. Lesson 4Current

    Section 13.4: Areas of Composite Figures

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