A parallelogram is a flat shape with opposite sides that are parallel and equal in length. A rhombus is a parallelogram with four equal (congruent) sides, such as a diamond. Squares and rectangles are also types of parallelograms. You can work out the height of a rhombus if you know other values, such as the area, base or diagonals.
TL;DR (Too Long; Didn't Read)
To find the height of a rhombus, use the formula height = area ÷ base. If you know the diagonals of a rhombus but not its area, use the formula area = (d1 x d2) ÷ 2, then apply the area to the first formula.
Properties of a Rhombus
No matter how large a rhombus is, certain rules always apply. All its sides are equal, its opposite angles are equal and its two diagonals are perpendicular (meaning they bisect each other at an angle of 90 degrees). The height of a rhombus (also called its altitude) is the shortest perpendicular distance from its base to its opposite side. The base of a rhombus can be any of its four sides, depending on how it is positioned.
Finding Height from Area and Base
The formula for the height of a rhombus is height = area ÷ base. For example, if you know the area of a rhombus is 64 cm2 and the base is 8 cm, you work out 64 ÷ 8 = 8. The height of the rhombus is 8 cm. Remember, the base is one of the sides and they are equal in length, so if you know the length of one of the sides, you know the length of them all.
The same formula applies regardless of the size of the rhombus or the units of measurement. For example, say you have a rhombus with an area of 1000 inches and a base of 20 inches. Work out 1000 ÷ 20 = 50. The height of the rhombus is 50 inches.
Finding Height from Diagonals
If you know the diagonals and base of a rhombus but not the area, use the formula area = (d1 x d2) ÷ 2. For example, if you know d1 is 4 cm and d2 is 6 cm, you work out (4 x 6) ÷ 2 = 12. You know the area is 12 cm2. If the base is 2 cm, work out 12 ÷ 2 = 6. The height of the rhombus is 6 cm.
References
Tips
- 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.
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Claire is a writer and editor with 18 years' experience. She writes about science and health for a range of digital publications, including Reader's Digest, HealthCentral, Vice and Zocdoc.