Lesson 9

Applying Area of Circles

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Lesson Narrative

In previous lessons, students estimated the area of circles on a grid and explored the relationship between the circumference and the area of a circle to see that \(A = \pi r^2\). In this lesson, students apply this formula to solve problems involving the area of circles as well as shapes made up of parts of circles (MP 1 and 2) and other shapes such as rectangles. These calculations require composition and decomposition recalling work from grade 6.

Also, in this lesson students are introduced to the idea of expressing exact answers in terms of \(\pi\).

Learning Goals

Teacher Facing

  • Calculate the area of a shape that includes circular or semi-circular parts, and explain (orally and in writing) the solution method.
  • Comprehend and generate expressions in terms of $\pi$ to express exact measurements related to a circle.

Student Facing

Let’s find the areas of shapes made up of circles.

Required Materials

Required Preparation

It is recommended that four-function calculators be made available to take the focus off computation.

Learning Targets

Student Facing

  • I can calculate the area of more complicated shapes that include fractions of circles.
  • I can write exact answers in terms of $\pi$.

CCSS Standards

Addressing

Glossary Entries

  • area of a circle

    If the radius of a circle is \(r\) units, then the area of the circle is \(\pi r^2\) square units.

    For example, a circle has radius 3 inches. Its area is \(\pi 3^2\) square inches, or \(9\pi\) square inches, which is approximately 28.3 square inches.

  • squared

    We use the word squared to mean “to the second power.” This is because a square with side length \(s\) has an area of \(s \boldcdot s\), or \(s^2\).