Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev

Mathematics (Maths) Class 9

Created by: Indu Gupta

Class 9 : Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev

The document Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev is a part of the Class 9 Course Mathematics (Maths) Class 9.
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Objective

To show that the area of rhombus is half the product of its diagonals.

Theory

  1. A rhombus is a simple (non-self-intersecting) quadrilateral whose all four sides are of same length.

  2. If a parallelogram has two consecutive sides congruent, it is a rhombus.

  3. If two triangles are congruent then their areas are equal.

  4. Area of a triangle = 1/2 X base X height

  5. Area of a rectangle = Length X Breadth

Proof

Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev

In above figure EHGF is rhombus with diagonal HF (length d1) and diagonal EG (length d2)

Area of rhombus EHGF = Area of triangle EFH + Area of triangle FH

    Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev
= half of the product of the diagonals

Example

Find the area of the following rhombus.

Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev

Solution:

In the given figure,

PR = d1= 24 cm.

SQ = d= 18 cm.

Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 Class 9 Notes | EduRev

\small = 216

So, the area of the rhombus PQRS is 216 cm2.

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