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6.3: Area of Parallelograms

Difficulty Level: At Grade Created by: CK-12
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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 \begin{align*}b\end{align*} units and height \begin{align*}h\end{align*} units, then the area, \begin{align*}A\end{align*}, is \begin{align*}bh\end{align*} square units.

\begin{align*}\text{Area} & = \text{base} \cdot \text{height}\\ A & = bh\end{align*}

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 \begin{align*}bh\end{align*}, so the area of the parallelogram is also \begin{align*}bh\end{align*}.

Warning: Notice that the height \begin{align*}h\end{align*} 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 \begin{align*}b\end{align*} units and height \begin{align*}h\end{align*} units, then the area, \begin{align*}A\end{align*}, is \begin{align*}bh\end{align*} square units.

\begin{align*}\text{Area} & = \text{base} \cdot \text{height}\\ A & = bh\end{align*}

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