Area Of Rhombus

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A rhombus is actually a parallelogram having four congruent sides. And when we talk of congruent sides, we mean matching, identical, or similar sides. The right word to use is ‘identical’ because the sides are the same. A rhombus doesn’t have to consist of right angles.

In a rhombus, there are four equal sides. The diagonals bisect one another at right angles. There are many ways or formulas you can use to calculate the area of rhombus and we will look at them.

Use of Diagonals

In a rhombus, the diagonals are those lines connecting the opposite corners or vertices through the center of the shape. There are two diagonals in a rhombus that run perpendicular and they tend to form four right angles at the center or the point of intersection.

So if you are given the diagonals as 6 cm and 10 cm, you can use this information to find the area of the rhombus.

Area of a rhombus = ½ab, where a is the value for one diagonal and b is the value for the other diagonal.

Area of the diagonal = ½ (6 x 10)

Area of the rhombus = ½ x 60

Area of the rhombus = 30 cm2

This is the formula you would want to use if you are given the diagonals or let’s say half the distances of the two diagonals.

But how do we come about getting this formula (½ ab)

Okay, let’s examine that…

In this figure, we take x to represent the diagonal labeled as PR; this is the longer diagonal. We also take y to represent the diagonal QS, which is the smaller diagonal.

If you look at the above figure, you can identify two triangles that form the rhombus. For example, triangle PQR and triangle PSR form the rhombus.

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Use of Base and Height

When you are given the height and the base, you can find the area. In this case, you are going to multiply the altitude of that rhombus with the base or length of the side of the shape. For example, if you are given the height as 10 cm and the base as 5 cm, you can use the information to calculate the area.

In this case, the formula of the rhombus will be:

Area of a Rhombus = height x base

Area of Rhombus = 10 x 5

Area of Rhombus = 50 cm 2

Use of Trigonometry

Since a rhombus has all four sides being equal, what you do is square the length of the side and multiply with sin of one angle. The formula will be:

Area of a Rhombus = s2 sin A, where s represents the length of one side and A represents the angle.

Let’s say that one side of a rhombus measures 5 cm and one angle measures 45 degrees, the area would be:

Area = s2 sin A

Area = 52 sin 45

Area = 25 x 0.71

Area = 17.75 cm2

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