# Area of a Parallelogram

## Base times height.

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Area of a Parallelogram

### Area of a Parallelogram

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*}. Be careful! The height of a parallelogram is always perpendicular to the base. This means that the sides are not the height.

#### Calculating the Area

Find the area of the parallelogram.

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

#### Solving for the Height

If the area of a parallelogram is \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.

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

#### Solving for the Width of the Base

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

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

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

### Examples

Find the area of the following shapes.

#### Example 1

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

#### Example 2

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

#### Example 3

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

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

### Review

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*} 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*} 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*}, 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*}, what is the base?

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### Vocabulary Language: English

TermDefinition
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).