How to Find the Perimeter of the Rhombus When the Diagonals Are Given

A square is just a rhombus with four right angles.

The diagonals of a rhombus, a parallelogram with four identical sides, bisect one another at 90-degree angles, creating four identical right triangles within the shape. Through Pythagoras' theorem, which explains that the hypotenuse --- the triangle's longest side that sits opposite its right angle --- equals the square root of the squares of the triangle's other legs added together, you can find the length of one side of the rhombus with one of the interior triangles, and then find the shape's perimeter.

Instructions

1. Divide both diagonals in half. For example, let the diagonals measure 6 and 8 inches. Half of 6 is 3 and half of 8 is 4.

2. Square both halves, then add the squares together. In this example, 3 squared is 9, and 4 squared is 16; 9 +16 = 25.

3. Calculate the square root of the previous step's sum to find the length of one of the rhombus' sides, and multiply the length by 4 to calculate its perimeter. Concluding this example, the square root of 25 is 5, and 5 multiplied by 4 is 20, so the rhombus' perimeter is 20 inches.

References

• Math Open Reference; Rhombus; John Page; 2009
• Coolmath.com: The Properties of a Rhombus
• Wolfram MathWorld; Pythagorean Theorem; Eric W. Weisstein