Illuminations: Area Formulas

Area Formulas
In this unit, students use the area formula for a rectangle to discover the area formulas for triangles, parallelograms, and trapezoids. Students also consider irregular figures whose areas can be determined by estimation or decomposition.

Prerequisite Knowledge

Students need to have a conceptual understanding of area, as well as some familiarity with the area formula for rectangles.

Individual Lessons

Lesson 1 - Discovering the Area Formula for Triangles

In this lesson, students develop the area formula for a triangle. Students find the area of rectangles and squares, and compare them to the areas of triangles derived from the original shape.

Lesson 2 - Finding the Area of Trapezoids

Students discover the area formula for trapezoids, as well as explore alternative methods for calculating the area of a trapezoid.

Lesson 3 - Finding the Area of Parallelograms

Students will use their knowledge of rectangles to discover the area formula for parallelograms.

Lesson 4 - Finding the Area of Irregular Figures

Students will estimate the areas of highly irregular shapes and will use a process of decomposition to calculate the areas of irregular polygons.

NCTM Resources

Learning and Teaching Measurement (2003 Yearbook)
National Council of Teachers of Mathematics Thinkfinity Verizon Foundation
More and Better Mathematics for All Students
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