Lesson Plan: Equality of the Areas of Two Parallelograms Mathematics

This lesson plan includes the objectives, prerequisites, and exclusions of the lesson teaching students how to identify parallelograms that have the same area when their bases are equal in length and the vertices opposite to these bases are on a parallel line to them.

Objectives

Students will be able to

• prove that two parallelograms between two parallel straight lines with a common base, or bases of equal length, have the same area,
• identify when two parallelograms have the same area,
• find the area of a parallelogram given the area of another parallelogram that shares the same base,
• find base lengths and heights of parallelograms given the area of another parallelogram,
• understand that a parallelogram and a rectangle that are between the same pair of parallel lines and share a common base have the same area,
• understand that if a triangle shares a base with a parallelogram and its other vertex lies on the opposite edge of the parallelogram, then the area of the triangle is half of that of the parallelogram.

Prerequisites

Students should already be familiar with

• finding the area of a parallelogram,
• finding the height of a parallelogram given its area and base length,
• finding the base length of a parallelogram given its area and height,
• finding the area of a triangle.

Exclusions

Students will not cover

• the equality of the areas of two triangles.