# High School Math : How to find the perimeter of a parallelogram

## Example Questions

### Example Question #1 : How To Find The Perimeter Of A Parallelogram

A parallelogram, with dimensions in cm, is shown below.

What is the perimeter of the parallelogram, in cm?

Explanation:

The triangle on the left side of the figure has a and a  angle. Since all of the angles of a triangle must add up to , we can find the angle measure of the third angle:

Our third angle is and we have a triangle.

A triangle has sides that are in the corresponding ratio of . In this case, the side opposite our angle is , so

We also now know that

Now we know all of our missing side lengths.  The right and left side of the parallelogram will each be . The bottom and top will each be . Let's combine them to find the perimeter:

### Example Question #2 : Parallelograms

Find the perimeter of the following parallelogram:

Explanation:

The formula for the perimeter of a trapezoid is:

,

where  is the length of the base and  is the length of the edge.

Opposite sides of a parallelogram have the same length. Therefore, both edges are  and both bases are .

Plugging in our values, we get:

### Example Question #3 : Parallelograms

Find the perimeter of the following parallelogram:

Explanation:

The formula for the perimeter of a parallelogram is:

where  is the length of the longer side and  is the length of the shorter side.

Plugging in our values, we get:

### Example Question #4 : Parallelograms

Find the perimeter of the following parallelogram:

Explanation:

The formula for the perimeter of a parallelogram is

.

Plugging in our values, we get:

### Example Question #1 : Quadrilaterals

ABCD is a parallelogram. BD = 5. The angles of triangle ABD are all equal. What is the perimeter of the parallelogram?