Find Perimeter of Rhombus from Diagonals | Geometry

How do we find the perimeter of a rhombus from the diagonals? If we're given the diagonals of a rhombus, we can find the perimeter pretty easily using the Pythagorean theorem, we'll see how in today's video geometry lesson!

All we need to do is recall a rhombus is an equilateral parallelogram. Since it is equilateral all of its sides are congruent, so we only need to find one side length then multiply that by four to get the perimeter. Since a rhombus is a parallelogram, its diagonals bisect each other. This allows us to prove that the diagonals also are perpendicular to each other, and so actually cut the rhombus into four congruent right triangles. Now we can simply use the Pythagorean theorem to solve for a side! Then multiply by 4! And that is the perimeter!

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