The perimeter of a rhombus is the total distance traveled along the edge of the rhombus. Recall that a rhombus is a two-dimensional figure with four equal sides and four angles that are not necessarily 90 degrees. A square can also be considered a rhombus since it satisfies all the conditions that a rhombus has.
A rhombus has the following conditions:
- All the sides have equal length.
- The opposite sides have to be parallel.
- Height is the perpendicular distance between two parallel sides.
- The diagonals of a rhombus bisect each other by 90 degrees.
Formula for the perimeter of a rhombus
A rhombus is a quadrilateral with four equal sides, one pair of opposite acute angles, and one pair of opposite obtuse angles. The formula for the perimeter of a rhombus is given as:
| p=4l |
where,
- p is the perimeter of the rhombus
- l is the length of one of the sides of the rhombus
Therefore, to calculate the perimeter, we just have to multiply by 4 the length of one of the sides of the rhombus.
Perimeter of a rhombus – Examples with answers
Apply the formula for the perimeter of a rhombus to solve the following examples. Each example has its respective solution, but it is recommended that you try to solve the examples yourself before looking at the answer.
EXAMPLE 1
Find the perimeter of a rhombus that has sides with a length of 7 m.
Solution
We have that the length of the sides of the rhombus is 7m. Therefore, we use this value in the perimeter formula:
$latex p=4l$
$latex p=4(7)$
$latex p=28$
The perimeter of the rhombus is 28 m.
EXAMPLE 2
What is the perimeter of a rhombus that has sides with a length of 12 m?
Solution
In this case, the length of the sides of the rhombus is 12 m. Using this value in the perimeter formula, we have:
$latex p=4l$
$latex p=4(12)$
$latex p=48$
The perimeter of the rhombus is 48 m.
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EXAMPLE 3
If the sides of a rhombus are 15 cm long, what is its perimeter?
Solution
We have that the length of a rhombus is 15 cm. We can calculate the perimeter of the rhombus with this length:
$latex p=4l$
$latex p=4(15)$
$latex p=60$
The perimeter of the rhombus is 60 m.
EXAMPLE 4
The perimeter of a rhombus is 36 m. What is the length of its sides?
Solution
In this case, we start with the perimeter of the rhombus and we want to obtain the length of its sides. We can use the value given in the formula and solve for l to be the length of one side:
$latex p=4l$
$latex 36=4l$
$latex l=9$
The length of one side of the rhombus is 9 m.
EXAMPLE 5
The perimeter of a rhombus is 68 cm. What is the length of one of its sides?
Solution
We can calculate the length of one of the sides by plugging the perimeter value into the formula and solving for l:
$latex p=4l$
$latex 68=4l$
$latex l=17$
The length of one of the sides is 17 cm.
Perimeter of a rhombus – Practice problems
Use what you have learned about the perimeter of a rhombus to solve the following problems. Select an answer and check it to make sure you selected the correct one.
See also
Interested in learning more about a rhombus? Take a look at these pages:
