Intermediate Geometry : How to find the perimeter of a rhombus

Study concepts, example questions & explanations for Intermediate Geometry

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Example Questions

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Example Question #31 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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.

 

Example Question #32 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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 #33 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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 #34 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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 #35 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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 #36 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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.

 

Example Question #37 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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.

Example Question #38 : How To Find The Perimeter Of A Rhombus

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

Possible Answers:

Correct answer:

Explanation:

13

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 #39 : How To Find The Perimeter Of A Rhombus

Given Rhombus  and diagonal 

Possible Answers:

Correct answer:

Explanation:

The rhombus referenced is below:

Rhombus

A diagonal of a rhombus bisects the angles of the rhombus at its endpoints. Therefore, since , it follows that  as well. By angle addition,

.

As consecutive angles of a rhombus (and, consequently, of a parallelogram),  and  are supplementary - that is, their measures total . Therefore,

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