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Example Question #71 : Quadrilaterals
If the area of a rhombus is 24 and one diagonal length is 6, find the perimeter of the rhombus.
The area of a rhombus is found by
A = 1/2(d1)(d2)
where d1 and d2 are the lengths of the diagonals. Substituting for the given values yields
24 = 1/2(d1)(6)
24 = 3(d1)
8 = d1
Now, use the facts that diagonals are perpendicular in a rhombus, diagonals bisect each other in a rhombus, and the Pythagorean Theorem to determine that the two diagonals form 4 right triangles with leg lengths of 3 and 4. Since 32 + 42 = 52, each side length is 5, so the perimeter is 5(4) = 20.