# Intermediate Geometry : How to find the perimeter of a rhombus

## Example Questions

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### Example Question #11 : Quadrilaterals

Given a rhombus with diagonal lengths of 12cm and 16cm, find the perimeter.

Explanation:

A rhombus is a parallelogram with all of its sides being equal. A square is a rhombus with all of the angles being equal as well as all of the sides. Both squares and rhombuses have perpendicular diagonal bisectors that split each diagonal into 2 equal pieces, and also splitting the quadrilateral into 4 equal right triangles.

With this being said, we know the Pythagorean Theorem would work great in this situation, using half of each diagonal as the two legs of the right triangle.

where  is the hypotenuse.

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We find the hypotenuse to be 10cm. Since the hypotenuse of each triangle is a side of the rhombus, we have found what we need to find the perimeter.

Each side is the same, so we add all 4 sides to find the perimeter.

### Example Question #12 : Quadrilaterals

The diagonals of a rhombus have lengths  and  units. What is its perimeter?

Explanation:

We should begin with a picture.

We should recall several things.  First, all four sides of a rhombus are congruent, meaning that if we find one side, we can simply multiply by four to find the perimeter.  Second, the diagonals of a rhombus are perpendicular bisectors of each other, thus giving us four right triangles and splitting each diagonal in half.  We therefore have four congruent right triangles.  Using Pythagorean Theorem on any one of them will give us the length of our sides.

With a side length of 17, our perimeter is easy to obtain.

Our perimeter is 68 units.

### Example Question #13 : Quadrilaterals

A rhombus has an area of  square units and an altitude of . Find the perimeter of the rhombus.

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

Then apply the perimeter formula:

, where  a side of the rhombus.

### Example Question #14 : Quadrilaterals

A rhombus has an area of  square units, and an altitude of . Find the perimeter of the rhombus.

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

Since, perimeter  , where  is equal to

Perimeter=

### Example Question #15 : Quadrilaterals

A rhombus has a side length of . Find the perimeter of the rhombus.

Explanation:

To find the perimeter, apply the formula: , where

### Example Question #16 : Quadrilaterals

A rhombus has an area of  square units, and an altitude of . Find the perimeter of the rhombus.

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

, where

### Example Question #17 : Quadrilaterals

Given that a rhombus has a side length of , find the perimeter of the rhombus.

Explanation:

To find the perimeter of this rhombus, apply the formula: , where

### Example Question #18 : Quadrilaterals

A rhombus has an area of  square units, and an altitude of . Find the perimeter of the rhombus.

Explanation:

In order to solve this problem, use the given information to work backwards to find a side length of the rhombus:

, where

### Example Question #19 : Quadrilaterals

A rhombus has a side length of  foot, what is the length of the perimeter (in inches).

inches

inches

inches

inches

feet

inches

Explanation:

To find the perimeter, first convert  foot into the equivalent amount of inches. Since,  and  is equal to  inches.

Then apply the formula , where  is equal to the length of one side of the rhombus.

Since,

The solution is:

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

Find the perimeter of a rhombus that has a side length of

Explanation:

In order to find the perimeter of this rhombus, first convert  from a mixed number to an improper fraction:

Then apply the formula: , where  is equal to one side of the rhombus.

Since,  the solution is:

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