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6.3: Area of Parallelograms

Difficulty Level: At Grade Created by: CK-12

Learning Objectives

  • Understand the basic concepts of the meaning of area.
  • Use formulas to find the area of parallelograms, including rectangles.

The area of a shape is the space inside the perimeter.

You can think of the perimeter as a line you may draw with a pen of the outer border of a shape. The area is what you would paint with a paintbrush in order to fill in the entire shape, painting inside the perimeter line.

For example,

In a fenced field, the fence would be the perimeter and the grass in the field would be the area.

In a basketball court, the sidelines would be the perimeter and the wooden court surface would be the area.

In a pool, the ________________ would be the perimeter and the ____________ would be the area.

Area of a Rectangle

If a rectangle has base b units and height h units, then the area, A, is bh square units.

\text{Area} & = \text{base} \cdot \text{height}\\A & = bh

Area of a Parallelogram

Example 1

How could we find the area of this parallelogram?

Make it into a rectangle by moving the triangular part:

The rectangle is made of the same parts as the parallelogram, so their areas are the same. The area of the rectangle is bh, so the area of the parallelogram is also bh.

Warning: Notice that the height h of the parallelogram is the perpendicular distance between two parallel sides of the parallelogram, not a side of the parallelogram (unless the parallelogram is also a rectangle, of course).

If a parallelogram has base b units and height h units, then the area, A, is bh square units.

\text{Area} & = \text{base} \cdot \text{height}\\A & = bh

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Date Created:

Feb 23, 2012

Last Modified:

May 12, 2014
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