A rhombus is a quadrilateral in Euclidean plane geometry, whose four sides have the same length. Often, a rhombus is called a diamond. Each rhombus is simple and is a special case of a kite and a parallelogram. A square is a rhombus with right angles. In a way, all squares can be considered rhombuses but every rhombus is not necessarily a square. Here, the concepts and formulas of a rhombus, like the formula of the area of a rhombus, are discussed in detail.
Area of Rhombus Formula
When dealing with Rhombus, the first question a student gets is How to find the area of a rhombus? Since we have a different formula to find an area of the rhombus.
Let’s discuss all formula of the rhombus briefly:
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Based on Side of the Rhombus Formula
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Area of rhombus when side and height is given
A = a * h
Where a = length of sides of the rhombus
h = height.
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Based on Diagonal of Rhombus Formula
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Area of Rhombus when diagonal of rhombus formula is given:
[A = frac{1}{2} times d_{1} times d_{2}]
Where d1 and d2 are the diagonals of the rhombus, the formula of diagonal of the rhombus is given as follows:
[d_{1} = sqrt{4a^{2} – d_{2}^{2}}]
[d_{2} = sqrt{4a^{2} – d_{1}^{2}}]
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Based on the Perimeter of the Rhombus Formula
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Rhombus area and perimeter formula are given:
A= 2*a*r
Where a = length of sides of the rhombus
r = radius of a circle inscribed in the rhombus
P= perimeter of rhombus= 4*a
Semiperimeter= 2*a
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Based on Height and Vertex Angle
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Area of Rhombus when height and vertex angle is given:
[A = frac{h^{2}}{sin alpha}]
Where h= height and α = vertex angle
Questions on the Area of Rhombus Formula:
1) Find the area of the rhombus when the side is 4 cm and the height is 6 cm.
Ans: Area of rhombus when side and height is given,
A = a * h
From question a = 4cm and h = 6cm. Substituting these values we get,
A = 4 * 6 = 24 cm2
2) The diagonals of the rhombus are given as 8 cm and 12 cm. Find the area of the rhombus.
Ans: Area of rhombus when diagonals are given,
[A = frac{1}{2} times d_{1} times d_{2}]
From question d1=8 cm and d2=12 cm. Substituting these values we get,
[A = frac{1}{2} times 8 times 12 = 48] cm2
Conclusion
The name “Rhombus” derives from the word “Rhombos” used in Ancient Greece. It means a piece of wood whirled to make a roaring noise on a string. We see rhombus-shaped figures every day today, in various spheres of life, hence it is very important to learn and understand the concepts of this shape.