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How to Find the Height of a Rhombus

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.

Things You'll Need

  • Calculator
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Instructions

  1. Given Side or Base and Area

    • 1

      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. Suppose a rhombus has an area of 25 cm and a base of 4 centimeters. Divide 25 by 4, obtaining 6.25.

    • 2

      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, then leave the answer 6.25.

    • 3

      Write the answer with the appropriate unit label, such as centimeters, inches or feet. In the example, write the solution as 6.25 cm, 6.3 cm or 6 cm, depending on the rounding specification.

    Given Side or Base and Diagonals

    • 4

      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*10 to get 240.

    • 5

      Divide this result by 2. In the example, divide 240 by 2, producing 120.

    • 6

      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.

    • 7

      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.

    • 8

      Include the unit label, such as inches, yards or centimeters, when writing your answer. In the sample problem, write the solution as 9.23 cm, 9.2 inches or 9 inches, according to the rounding specification.

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