# How Do You Find the Perimeter and Area of a Rhombus?

We have previously seen that rectangles and the squares have a few things in common, and that squares are a special case of rectangles with all equal sides. The same is true for parallelograms and rhombuses. A rhombus is to a parallelogram as a square is to a rectangle—the rhombus is a special type of parallelogram. A rhombus is a quadrilateral where each set of two sides are parallel to each other, and all sides are of equal length.

## Perimeter of a Rhombus

To find the perimeter of a rhombus you must find the sum of all the sides. In a rhombus all the sides are of equal length, so you only need to know one of the lengths and then multiply it by four.

Formula

### PerimeterofaRhombus

Two and two sided are parallel $\begin{array}{llll}\hfill P& =4\cdot \text{side}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =4\cdot s\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 1

Find the perimeter of the rhombus

You follow the formula and times the length of one side with 4:

 $P=4\cdot 5\phantom{\rule{0.17em}{0ex}}\text{cm}=20\phantom{\rule{0.17em}{0ex}}\text{cm}$

## Area of a Rhombus

A rhombus is really a square that has been shifted at the top or the bottom. If you straightened it out so that all the angles were $90$°, you would get a square.

To find the area of a rhombus, you need to know the length of one of the sides—the base—and the height of the rhombus. The height is always perpendicular to the base and the side opposite it. When you have both the base and the height, you use the same formula as for the rectangle, and multiply the base by the height.

Formula

### AreaofaRhombus

$\begin{array}{llll}\hfill A& =\text{base}\cdot \text{height}\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\\ \hfill & =b\cdot h\phantom{\rule{2em}{0ex}}& \hfill & \phantom{\rule{2em}{0ex}}\end{array}$

Example 2

Find the area of the rhombus

You find the area by using the equation:

 $A=5\phantom{\rule{0.17em}{0ex}}\text{cm}\cdot 4\phantom{\rule{0.17em}{0ex}}\text{cm}=20\phantom{\rule{0.17em}{0ex}}{\text{cm}}^{2}$