# 5.10: Area of a Parallelogram

- Page ID
- 4994

Use \(A=bh\) to find area.

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 \(A=bh\). The height of a parallelogram is always perpendicular to the base. This means that the sides are not the height.

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?

Example \(\PageIndex{1}\)

Find the area of the parallelogram.

**Solution**

Area is \(15(6)=90\text{ un}^2\).

Example \(\PageIndex{2}\)

Find the area of the parallelogram with a base of 10 m and a height of 12 m.

**Solution**

Area is 10(12)=120\text{ m}^2\).

Example \(\PageIndex{3}\)

Find the area of the parallelogram.

**Solution**

\(A=15\cdot 8=120 \text{ in}^2\)

Example \(\PageIndex{4}\)

If the area of a parallelogram is \(56 \text{ units }^2\) and the base is 4 units, what is the height?

**Solution**

Solve for the height in \(A=bh\).

\(56\text{ units }=4h\)

\(14 \text{ units }=h\)

Example \(\PageIndex{5}\)

If the height of a parallelogram is 12 m and the area is \(60 m^2\), how wide is the base?

**Solution**

Solve for the base in \(A=bh\).

\(60 \text{ units } =12b\)

\(5 \text{ units } =b\)

## Review

- 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 \(42\text{ units }^2\) and the base is \(6\text{ units }\), what is the height?
- If the area of a parallelogram is \(48\text{ units }^2\) and the height is \(6\text{ units }\), what is the base?
- If the base of a parallelogram is 9 units and the area is \(108\text{ units }^2\), what is the height?
- If the height of a parallelogram is 11 units and the area is \(27.5\text{ units }^2\), what is the base?

## Vocabulary

Term | Definition |
---|---|

area |
The amount of space inside a figure. Area is measured in square units. |

perimeter |
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. |

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). |

## Additional Resources

Interactive Element

Video: Area of a Parallelogram (Whole Numbers)

Activities: Area of a Parallelogram Discussion Questions

Study Aids: Triangles and Quadrilaterals Study Guide

Practice: Area of a Parallelogram

Real World: Perimeter