What if you were given a parallelogram and the size of its base and height? How could you find the amount of space the parallelogram takes up? After completing this Concept, you'll be able to use the formula for the area of a parallelogram to solve problems like this one.

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### Guidance

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*}. 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*}

#### Example B

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

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

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

#### Example C

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*}

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### 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*}.

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

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

### Explore More

- Find the area of a parallelogram with height of 20 m and base of 18 m.
- Find the area of a parallelogram with height of 12 m and base of 15 m.
- Find the area of a parallelogram with height of 40 m and base of 33 m.
- Find the area of a parallelogram with height of 32 m and base of 21 m.
- Find the area of a parallelogram with height of 25 m and base of 10 m.

Find the area of the parallelogram.

- If the area of a parallelogram is \begin{align*}42 \ units^2\end{align*} and the base is 6 units, what is the height?
- If the area of a parallelogram is \begin{align*}48 \ units^2\end{align*} and the height is 6 units, what is the base?
- If the base of a parallelogram is 9 units and the area is \begin{align*}108 \ units^2\end{align*}, what is the height?
- 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?

### Answers for Explore More Problems

To view the Explore More answers, open this PDF file and look for section 10.2.