What Is the Procedure To Find Out the Area of the Rhombus?
The rhombus is a four-sided quadrilateral that has equal sides. It looks like a diamond in shape. Moreover, its sides are congruent to each other. It has similar properties to a parallelogram where the opposite sides are parallel, opposite angles are equal and adjacent angles add up to 180 degrees.
The area of rhombus refers to the space enclosed within the four sides that can be easily calculated in three different ways. It’s calculated in cm or m squares depending upon the value of length. There are various ways through which the area of a Rhombus can be calculated. The formula and method to be used depending on the value of the Rhombus known at hand.
1. Area of Rhombus Through Diagonals:
A Rhombus is similar to a square in terms of various properties like equal and parallel sides, adjacent supplementary angles, etc. The area of a Rhombus can be easily calculated through the use of its diagonals. A rhombus has two diagonals that intersect each other at a common point and right angles. This results in the creation of 4 right-angled triangles. Also, the area of a right-angled triangle is 1/2 x base x height.
Through derivation and addition of 4 right angle triangles, the area of Rhombus can be calculated as – 1/2 x Diagonal 1 x Diagonal 2.
Multiplying both the diagonals of a Rhombus and dividing the result by 2 can help in arriving at the area of the Rhombus.
If the length of one side and a diagonal is known then the value of the second diagonal can be easily found through the use of the Pythagoras theorem.
For example – The length of the two diagonals of the rhombus are 5 cm and 10 cm respectively. The area of the rhombus can be easily calculated by using the formula – 1/2 x Diagonal 1 x Diagonal 2.
Area of Rhombus = 1/2 x 5 x 10 = 25 cm^2.
2. Area of Rhombus Through Use of Base and Height:
The area of a Rhombus can also be calculated through the use of the length of base and height. The base of a Rhombus refers to its side. All the sides are equal in length, which means any side can be taken as a base.
The height is the distance between two sides that are opposite to each other. The distance here refers to the perpendicular distance between two opposite sides.
The height of the Rhombus and the length of its base are multiplied with each other which results in the area of a Rhombus. Mathematically Area of Rhombus = base x height.
For example, the length of base and height of a Rhombus is 15 cm and 20 cm respectively. Area of Rhombus = base x height
= 15 x 20 cm = 300 cm^2
3. Area of Rhombus Through Use of Trigonometry:
Another way of calculating the area of the Rhombus is to use Trigonometry. The area of Rhombus can be calculated through the formula – (side) ^2 x sin (a) where a is the value of angle that any two sides make with each other.
Steps for calculating the area of the rhombus through the use of trigonometry:
Step 1. Find out the length of the base and angle between the two sides.
Step 2. Input the value of base and angle into the formula (side) ^2 x sin (a) to arrive at the area of Rhombus.
For example – The length of the base of the rhombus is 4 cm and the angle between the two sides is 30°. The area of the rhombus can be calculated through the use of the formula – (side) ^2 x sin (a).
Area of rhombus = (4) ^2 x sin (30)
= 16 x 1/2
= 8 cm^2
Calculating the area of a rhombus is quite simple if one is aware of its measures and formulas. Cuemath makes the process of understanding different properties of a rhombus, area derivation, and obtaining knowledge about various other geometrical shapes easy and hassle-free.
Thank you,
Glenda, Charlie and David Cates
