Rhombus Area Calculator

Area is a numerical characteristic of a two-dimensional (flat or curved) geometric figure, informally speaking, showing the size of this figure. Historically, the calculation of the area was called quadrature. A figure having an area is called quadratic. Find the area of more than 22 shapes (triangle, square, pentagon, etc.) using our amazing calculator.

Rhombus — is called a parallelogram, in which all sides are equal. Since the rhombus is a parallelogram, it has all the properties of a parallelogram.

A rhombus is a four-sided polygon with all sides equal in length. To calculate the area of a rhombus, our calculator offers three methods: by the diagonals, by the side and corner, and through the base and height. Below are the formulas for calculating the area of a rhombus using each method:

Calculating Rhombus Area by Diagonals:

The area of a rhombus can be calculated using its diagonals, represented as d₁ and d₂, using the formula:

S = \dfrac{1}{2}*d_1*d_2

This formula is derived from the fact that a rhombus can be divided into four congruent right triangles, each with base and height equal to half the length of the diagonals.

Calculating Rhombus Area by Side and Corner:

The area of a rhombus can also be calculated using the length of one side (a) and the measure of one angle (α) using the formula:

S = a^2*sin(α)

This formula is derived from the fact that the area of a triangle can be calculated using the formula (1/2) × base × height, where the base is equal to a side of the rhombus and the height is equal to half the length of a diagonal. Since the diagonals of a rhombus are perpendicular bisectors of each other, the angle between them is 90 degrees, and sin(α) is equal to the ratio of the length of one diagonal to the length of the other.

Calculating Rhombus Area through Base and Height:

The area of a rhombus can also be calculated using the length of its base (a) and the perpendicular distance from the base to the opposite side (h), using the formula:

S = ah

This formula is derived from the fact that the area of a parallelogram can be calculated using the formula base × height, where the base is equal to one side of the rhombus and the height is equal to the perpendicular distance between the base and the opposite side.

To use our rhombus area calculator, simply choose the appropriate method and enter the required measurements. Our calculator will do the rest!

Example:

Suppose we have a rhombus with diagonals d₁ = 8 and d₂ = 10. To find the area, we can use the formula:

A = (8 × 10) / 2 = 40

So the area of the rhombus is 40 square units.

Calculating the area of a rhombus is an essential skill in geometry. Our rhombus area calculator and formulas make it easy to find the area of your rhombus. Try it out for yourself and see how easy it can be!