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

## Example Questions

### Example Question #21 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve and round to two decimal places.

### Example Question #22 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve.

### Example Question #23 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve and round to two decimal places.

### Example Question #24 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve and round to two decimal places.

### Example Question #25 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve and round to two decimal places.

### Example Question #26 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has diagonals of the following lengths:  and .

Explanation:

Recall that the diagonals of a rhombus bisect each other and are perpendicular to one another.

In order to find the length of the side, we can use Pythagorean's theorem. The lengths of half of the diagonals are the legs, and the length of the side of the rhombus is the hypotenuse.

First, find the lengths of half of the diagonals.

Next, substitute these half diagonals as the legs in a right triangle using the Pythagorean theorem.

Since the sides of a rhombus all have the same length, multiply the side length by  in order to find the perimeter.

Solve and round to two decimal places.

### Example Question #31 : Rhombuses

Find the perimeter of a rhombus if it has an area of  and a diagonal of .

Explanation:

Recall the following properties of a rhombus, as shown by the figure above: The diagonals of a rhombus are perpendicular and they bisect each other. Thus, if we know the lengths of the diagonals, we can use the Pythagorean theorem to find the length of a side of the rhombus.

Recall how to find the area of a rhombus:

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

Plug in the given values to find the length of the second diagonal.

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

Make sure to round to  places after the decimal.

### Example Question #28 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of  and a diagonal of .

Explanation:

Recall the following properties of a rhombus, as shown by the figure above: The diagonals of a rhombus are perpendicular and they bisect each other. Thus, if we know the lengths of the diagonals, we can use the Pythagorean theorem to find the length of a side of the rhombus.

Recall how to find the area of a rhombus:

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

Plug in the given values to find the length of the second diagonal.

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

Make sure to round to  places after the decimal.

### Example Question #29 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus if it has an area of  and a diagonal of .

Explanation:

Recall the following properties of a rhombus, as shown by the figure above: The diagonals of a rhombus are perpendicular and they bisect each other. Thus, if we know the lengths of the diagonals, we can use the Pythagorean theorem to find the length of a side of the rhombus.

Recall how to find the area of a rhombus:

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

Plug in the given values to find the length of the second diagonal.

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

Make sure to round to  places after the decimal.

### Example Question #30 : How To Find The Perimeter Of A Rhombus

Find the perimeter of a rhombus that has an area of  and a diagonal of .

Explanation:

Recall the following properties of a rhombus, as shown by the figure above: The diagonals of a rhombus are perpendicular and they bisect each other. Thus, if we know the lengths of the diagonals, we can use the Pythagorean theorem to find the length of a side of the rhombus.

Recall how to find the area of a rhombus:

Since we are given the length of one diagonal and the area, we can find the length of the second diagonal.

Plug in the given values to find the length of the second diagonal.

Now, notice that the halves of each diagonal make up a right triangle that has the side length of the rhombus as its hypotenuse.

Now, use these half values in the Pythagorean Theorem to find the length of the side of a rhombus.

Finally, recall that a rhombus has four equal side lengths. To find the perimeter, multiply the length of a side by four.

Make sure to round to  places after the decimal.