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Area of a Parallelogram

Base times height.

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Area of a Parallelogram

What if you wanted to find the area of a parallelogram? How does the area of a parallelogram relate to the area of a rectangle? After completing this Concept, you'll be able to solve problems like these.

Watch This

CK-12 Foundation: Chapter10AreaofaParallelogramA

Learn more about the area of parallelograms by watching the video at this link.

Guidance

Recall that a parallelogram is a quadrilateral whose opposite sides are parallel.

To find the area of a parallelogram, make it into a rectangle.

From this, we see that the area of a parallelogram is the same as the area of a rectangle. The area of a parallelogram is \begin{align*}A=bh\end{align*}A=bh. Be careful! The height of a parallelogram is always perpendicular to the base. This means that the sides are not the height.

Example A

Find the area of the parallelogram.

\begin{align*}A=15 \cdot 8=120 \ in^2\end{align*}A=158=120 in2

Example B

If the area of a parallelogram is \begin{align*}56 \ units^2\end{align*}56 units2 and the base is 4 units, what is the height?

Plug in what we know to the area formula and solve for the height.

\begin{align*}56 &= 4h\\ 14 &= h\end{align*}5614=4h=h

Example C

If the height of a parallelogram is \begin{align*}12 \ m\end{align*}12 m and the area is \begin{align*}60 \ m^2\end{align*}60 m2, how wide is the base?

Solve for the base in \begin{align*}A=bh\end{align*}A=bh.

\begin{align*}60 \ units &= 12b\\ 5 \ units &= b\end{align*}60 units5 units=12b=b

Watch this video for help with the Examples above.

CK-12 Foundation: Chapter10AreaofaParallelogramB

Vocabulary

Perimeter is the distance around a shape. The perimeter of any figure must have a unit of measurement attached to it. If no specific units are given (feet, inches, centimeters, etc), write “units.” Area is the amount of space inside a figure. Area is measured in square units. A parallelogram is a quadrilateral whose opposite sides are parallel.

Guided Practice

Find the area of the following shapes.

1.

2.

3. A parallelogram with a base of 10 m and a height of 12 m.

Answers:

1. Area is \begin{align*}15(6)=90 \ un^2\end{align*}15(6)=90 un2.

2. Area is \begin{align*}32(12)=672 \ un^2\end{align*}32(12)=672 un2.

3. Area is \begin{align*}10(12)=120 \ m^2\end{align*}10(12)=120 m2.

Interactive Practice

Practice

  1. Find the area of a parallelogram with height of 20 m and base of 18 m.
  2. Find the area of a parallelogram with height of 12 m and base of 15 m.
  3. Find the area of a parallelogram with height of 40 m and base of 33 m.
  4. Find the area of a parallelogram with height of 32 m and base of 21 m.
  5. Find the area of a parallelogram with height of 25 m and base of 10 m.

Find the area of the parallelogram.

  1. If the area of a parallelogram is \begin{align*}42 \ units^2\end{align*}42 units2 and the base is 6 units, what is the height?
  2. If the area of a parallelogram is \begin{align*}48 \ units^2\end{align*}48 units2 and the height is 6 units, what is the base?
  3. If the base of a parallelogram is 9 units and the area is \begin{align*}108 \ units^2\end{align*}108 units2, what is the height?
  4. If the height of a parallelogram is 11 units and the area is \begin{align*}27.5 \ units^2\end{align*}27.5 units2, what is the base?

Vocabulary

Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides.

Area of a Parallelogram

The area of a parallelogram is equal to the base multiplied by the height: A = bh. The height of a parallelogram is always perpendicular to the base (the sides are not the height).

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