A rhombus is a special type of parallelogram in which all four sides possess equal lengths and opposite sides run parallel to each other. A baseball diamond is an example of a rhombus because the distance between each of the four bases is the same. The height of a rhombus is also called its altitude. This is the shortest perpendicular distance from the base of the rhombus to its opposite side. When working with rhombi, the terms “side” and “base” are interchangeable – that is, any side can be designated a base.
Given Side or Base and Area
Divide the area by the length of the side or base. Remember, all sides are equal in a rhombus, so it doesn’t matter which side length is given. For example, suppose a rhombus has an area of 25 square centimeters and a base of 4 centimeters. Divide 25 by 4, which yields 6.25.
Round, if directed by the problem to do so. In the example, if asked to round to the nearest tenth, round to 6.3. If asked to round to the nearest integer or whole number, round to 6. If not asked to round, leave the answer 6.25.
Write the answer with the appropriate unit label, such as centimeters, inches or feet. In the example, write the solution as 6.25 centimeters, 6.3 centimeters or 6 centimeters, depending on the rounding specification.
Given Side or Base and Diagonals
Multiply the lengths of the diagonals. Suppose the problem states that one diagonal has a length of 24 inches and the other has a length of 10 inches. Multiply 24 by 10 to get 240.
Divide this result by 2. In the example, divide 240 by 2, producing 120.
Divide this number by the length of the side, or base. Suppose in the example that the length of a side or base is given as 13 inches. Divide 120 by 13, obtaining approximately 9.23.
Round as directed in the problem. In the example, if asked to round to the nearest tenth, round to 9.2 inches. If asked to round to the nearest integer or whole number, round to 9 inches.
Include the unit label, such as inches, yards or centimeters, when writing your answer. In the sample problem, write the solution as 9.23 inches, 9.2 inches or 9 inches, according to the rounding specification.
TL;DR (Too Long; Didn't Read)
A square is actually a special type of rhombus whose sides aren’t slanted -- that is, all four sides join each other at 90-degree angles. The height of a square is equal to the length of any of its sides.