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Rhombus - Geometric Properties and Area of Rhombus Formula

 

We are all familiar with the shape of a 2D diamond. In Euclidean geometry, this shape is known as a rhombus. A rhombus is a quadrilateral (having four sides) of equal lengths but in the shape of a parallelogram. It is a particular instance of a parallelogram in which the diagonals cross at 90 degrees.

The diagonals of the rhombus bisect its interior angles and form 4 right-angle isosceles triangles, which are similar and congruent to each other. The adjacent angles of a rhombus equal 180 degrees in value, and all four angles together constitute 360 degrees. Now that we have discussed some major characteristics like the shape, angles, and diagonals of a rhombus, let us discuss the important parameters like the perimeter and area of a rhombus.

Area: The area of a rhombus is described as the amount of space swept by the rhombus in the 2D plane. The area of a rhombus is formulated as ½ (diagonal 1 x diagonal 2). The lengths of the diagonals determine the area of the rhombus. Perimeter: The perimeter of a rhombus is the total distance of its boundaries. Just like the perimeter of a square with side ‘s’, the perimeter of a rhombus with each side ‘l’ is written as 4l.

Geometric Properties of a Rhombus:

Let us now learn about the various properties of a rhombus. They are mentioned below:

  • If the midpoints of both diagonals are joined together, then the resulting figure will be another rhombus. When the midpoints of each side are connected, the resulting shape is a rectangle. The rectangle's length and breadth will be exactly half of the value of the major diagonal, and its area will be half that of the rhombus.
  • There are neither inscribing circles within a rhombus nor circumscribing circles outside the perimeters of a rhombus.
  • Two congruent equilateral triangles are produced when the shorter diagonal equals one of the rhombus's sides.
  • On rotating a rhombus about either side of the axis of rotation, you will receive a cylindrical surface with a convex cone at one end and a concave cone at the other.
  • When the rhombus is rotated around the line connecting the midpoints of the opposing sides as the axis of rotation, a cylindrical surface is obtained with concave cones on either end.
  • When a rhombus revolves around the longer diagonal about the axis of rotation, a solid with two cones linked to their bases is obtained. In this example, the solid's greatest diameter is equal to the rhombus's shorter diagonal.
  • When a rhombus revolves around the longer diagonal about the axis of rotation, a solid with two cones linked to their bases is obtained. In this example, the solid's greatest diameter is equal to the rhombus's shorter diagonal.
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