Perimeter and Area of Rhombus
Maths plays a key role in your higher learning and entrance examinations. Whether it is for your entrance examinations, or your school and board examinations, the knowledge of Mathematics is essential for one to succeed in his or her ambitions. One such topic from the chapter on Area and Perimeter is to calculate the area of a rhombus.
In Euclidean geometry, A Rhombus is a quadrilateral that has four edges and four corners and all 4 edges are equal in length. All rhombuses are parallelograms, which mean both the adjacent edges are parallel to each other. The interesting point to note here is that a rhombus whose corners are at the right angle is known as a square.
The formula for Calculating the Area and perimeter of a Rhombus
The three ways to calculate the area of a diamond are diagonal, floor and height, and trigonometry. Some important properties of diamond are:
All sides are the same length. The other side is also parallel to each other. The height is the vertical distance between two parallel sides. The two diagonals of a diamond are halved at 90 degrees. The formula for the circumference of a diamond is very easy to calculate. That is, the circumference or P = 4 × a. Where "a" is the length of one side of the diamond. Diagonal diamond area:
In the diagonal method, the diamond area can be calculated using the following formula:
A = ½ × d1 × d2.
Wo,
A = Area of diamond. d1 =
Diagonal length d1.
d2 =
Diagonal length d2.
If any of these values are available, the area and circumference of the diamond can also be calculated. In other words, given the area, the perimeter can also be calculated. The reverse method is also possible.
How to find the Area of a Rhombus?
Area of a rhombus can be derived in 3 ways:
Using diagonals – A = ½ × d1 × d2.
Using Base and Height – A = b × h.
Using trigonometry – A = b2 × Sin(a).
Where
d1 = Length of diagonal 1.
d2 = Length of diagonal 2.
b = Length of any side.
h = Height of rhombus.
a = Measure of interior angle.
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FAQs on Area of a Rhombus Formula
What is a parallelogram?
In geometry, you will come across many shapes and sizes which you have to study to gain a perspective on how to calculate the area and perimeter of certain objects. The most important shapes in Euclidean geometry are the triangle, circle, and quadrilateral. In the triangle, you have an obtuse angle triangle, right-angle triangle, acute angle triangle, etc. Similarly in Quadrilaterals, when the two opposite sides are parallel to each other, it is known as a parallelogram.
What do we mean by area and perimeter?
The terms area and perimeter are important quantities that describe the characteristics of space occupied by a certain object. The perimeter can simply be said as the measure of the outer edge of an object which runs throughout the shape of the body and provides it with a certain shape. The area, however, does not specifically depend on boundary conditions and is measured as the space occupied by the enclosed boundaries of a body.
Why is the importance of the rhombus?
The rhombus is a very essential object in Euclidean geometry as it signifies one of the types of a parallelogram in which all sides are equal. Now in a body where all sides are equal, the shape is by default going to be a parallelogram but many confuse that shape with a square. A square is a certain condition of a rhombus and hence while all squares are rhombuses, all rhombuses may not necessarily be squares.
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I am having trouble while solving questions on rhombus, what shall I do?
The rhombus is a very important part of Euclidean geometry and students must have good command over the topic as questions regarding this shape come regularly in school examinations and also in entrance level examinations like the JEE Mains and JEE Advanced. Try asking your doubts to your teachers when the subject is being taught in the class. You can access the online study materials at Vedantu which are designed in a student-friendly way to ensure a proper understanding of the basics of the topic and the exercises have been provided with step-by-step solutions.
