Related Topics:

Lesson Plans and Worksheets for Geometry

Lesson Plans and Worksheets for all Grades

More Lessons for Geometry

Common Core For Geometry

Student Outcomes

- Students review the area formula for rectangles with rational side lengths and prove the area formula for an arbitrary rectangle.
- Students use a square grid to estimate the area of a curved region using lower approximations, upper approximations, and average approximations.

**What Is Area?**

Classwork

**Exploratory Challenge 1**

a. What is area?

b. What is the area of the rectangle below whose side lengths measure 3 units by 5 units?

c. What is the area of the 3/4 × 5/3 rectangle below?

**Exploratory Challenge 2**

a. What is the area of the rectangle below whose side lengths measure √3 units by √2 units? Use the unit squares on the graph to guide your approximation. Explain how you determined your answer. b. Is your answer precise?

**Discussion**

Use Figures 1, 2, and 3 to find upper and lower approximations of the given rectangle.

**Discussion**

If it takes one can of paint to cover a unit square in the coordinate plane, how many cans of paint are needed to paint the region within the curved figure?

Try the free Mathway calculator and
problem solver below to practice various math topics. Try the given examples, or type in your own
problem and check your answer with the step-by-step explanations.

We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.