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In A Rhombus Of Side 10Cm

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in a rhombus of side 10cm one of the diagonals is 12 cm long find the
in a rhombus of side 10cm one of the diagonals is 12 cm long find the from brainly.in

As we delve deeper into the world of geometry, we come across various shapes and figures that seem to be simple but hold a lot of importance in the field. One such shape is a rhombus, which is a four-sided figure whose sides are equal in length. In this article, we will discuss everything you need to know about a rhombus of side 10cm.

Definition of a Rhombus

A rhombus is a quadrilateral whose four sides are equal in length. It is also known as a diamond or a lozenge. The opposite angles of a rhombus are equal, and the diagonals bisect each other at right angles. A rhombus can be thought of as a special case of a parallelogram where all the sides are equal.

Properties of a Rhombus of Side 10cm

Let us consider a rhombus of side 10cm. Here are some of its properties:

  • All four sides are equal in length, i.e., 10cm each.
  • Opposite angles are equal.
  • The diagonals bisect each other at right angles.
  • The area of the rhombus is given by the formula: Area = (diagonal 1 x diagonal 2)/2.
  • The perimeter of the rhombus is 40cm.

    • Calculating the Area of a Rhombus of Side 10cm

    To calculate the area of a rhombus of side 10cm, we need to know the length of its diagonals. Let us assume that the diagonals are d1 and d2. Using the formula mentioned above, we can calculate the area as:

    Area = (d1 x d2)/2

    As the diagonals of a rhombus bisect each other at right angles, we can use the Pythagorean theorem to find the length of the diagonals. Let us assume that half of one diagonal is a (5cm) and the other half is b (5cm). Then, using the Pythagorean theorem, we can find the length of the diagonals as:

    d1 = d2 = √(a2 + b2) = √(52 + 52) = √50cm

    Therefore, the area of the rhombus is:

    Area = (d1 x d2)/2 = (√50 x √50)/2 = 25cm2

    Calculating the Perimeter of a Rhombus of Side 10cm

    The perimeter of a rhombus is the sum of the lengths of all its sides. As all the sides of a rhombus are equal, we can simply multiply the length of one side by 4 to get the perimeter. Therefore, the perimeter of a rhombus of side 10cm is:

    Perimeter = 4 x 10cm = 40cm

    Applications of Rhombus

    The rhombus is a common shape found in various fields. Here are some of its applications:

  • In jewelry making, rhombus-shaped stones are used to create beautiful designs.
  • In architecture, rhombus-shaped tiles are used to create unique patterns on walls and floors.
  • In engineering, rhombus-shaped brackets are used to provide support to various structures.
  • In mathematics, rhombus is used to teach concepts like congruence, similarity, and area.

    • Conclusion

    A rhombus is a simple but important shape in geometry. It is a four-sided figure whose sides are equal in length. A rhombus of side 10cm has various properties like equal opposite angles, diagonals bisecting each other at right angles, and an area of 25cm2. The rhombus finds its application in various fields like jewelry making, architecture, engineering, and mathematics. Understanding the properties and applications of a rhombus can help us appreciate the importance of geometry in our daily lives.

    So, next time you come across a rhombus, you know what to look for!

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