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# 10.2: Area of a Parallelogram

Difficulty Level: At Grade Created by: CK-12
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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.

### 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 A=bh\begin{align*}A=bh\end{align*}. 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.

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

#### Example B

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

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

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

#### Example C

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

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

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

Watch this video for help with the Examples above.

### 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.

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

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

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

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

### Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes

### Vocabulary Language: English

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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