Lesson 4


Let’s investigate the features and area of parallelograms.

4.1: Features of a Parallelogram

Figures A, B, and C are parallelograms. Figures D, E, and F are not parallelograms. 

Six figures on a grid labeled A--F.

Study the examples and non-examples. What do you notice about:

  1. the number of sides that a parallelogram has?
  2. opposite sides of a parallelogram?
  3. opposite angles of a parallelogram?

4.2: Area of a Parallelogram

  1. Find the area of the parallelogram and explain your reasoning.

  2. Change the parallelogram by dragging the green points at its vertices. Find its area and explain your reasoning.

  3. If you used the polygons on the side, how were they helpful? If you did not, could you use one or more of the polygons to show another way to find the area of the parallelogram?

4.3: Lots of Parallelograms

Find the area of each parallelogram. Show your reasoning.

Two figures on a grid: parallelogram A and parallelogram B.
Parallelogram C has base 6, height 4, and diagonal length 4.5.


A parallelogram is a quadrilateral (it has four sides). The opposite sides of a parallelogram are parallel. It is also true that the opposite sides of a parallelogram have equal length, and the opposite angles of a parallelogram have equal measure.

Two paralllelograms with the angles and side lengths provided.

There are several strategies for finding the area of a parallelogram.

  • We can decompose and rearrange a parallelogram to form a rectangle. Here are three ways:
    Three identical parallelograms on separate grids, each has a base of four units and a height of three units.
  • We can enclose the parallelogram and then subtract the area of the two triangles in the corner.
    Two drawings of parallelograms on grids.

Both of these ways will work for any parallelogram. However, for some parallelograms the process of decomposing and rearranging requires a lot more steps than if we enclose the parallelogram with a rectangle and subtract the combined area of the two triangles in the corners.

A shaded parallelogram on a grid decomposed and rearranged into a rectangle.

Glossary Entries

  • parallelogram

    A parallelogram is a type of quadrilateral that has two pairs of parallel sides.

    Here are two examples of parallelograms.

    Two paralllelograms with the angles and side lengths provided.
  • quadrilateral

    A quadrilateral is a type of polygon that has 4 sides. A rectangle is an example of a quadrilateral. A pentagon is not a quadrilateral, because it has 5 sides.