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Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 | Extra Documents & Tests for Class 9 PDF Download

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 | Extra Documents & Tests for Class 9

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 | Extra Documents & Tests for Class 9
= 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 | Extra Documents & Tests for Class 9

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 | Extra Documents & Tests for Class 9

\small = 216

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

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FAQs on Procedure - To show that the Area of Rhombus is half the Product of its Diagonals, Math, Class 9 - Extra Documents & Tests for Class 9

1. What is the formula to calculate the area of a rhombus?
Ans. The formula to calculate the area of a rhombus is given by: Area = (diagonal1 * diagonal2) / 2, where diagonal1 and diagonal2 are the lengths of the diagonals of the rhombus.
2. How do you find the length of the diagonals of a rhombus?
Ans. To find the length of the diagonals of a rhombus, you can use the Pythagorean theorem. If the rhombus has side length 'a' and one angle measures 'θ', then the length of the diagonals can be calculated as: diagonal1 = a * √(2 + 2 * cosθ) and diagonal2 = a * √(2 - 2 * cosθ).
3. Can a rhombus have diagonals of different lengths?
Ans. No, in a rhombus, both diagonals are of equal length. This is because a rhombus is a special type of parallelogram, and opposite sides of a parallelogram are always congruent. Therefore, the diagonals, which bisect each other and connect opposite vertices, must have the same length.
4. How can I find the area of a rhombus if only one diagonal is given?
Ans. If only one diagonal of a rhombus is given, you can find the area by using the formula: Area = (diagonal^2) / 2. Simply square the length of the given diagonal and divide it by 2 to calculate the area of the rhombus.
5. What are some real-life applications of the concept of rhombus area?
Ans. The concept of rhombus area is used in various real-life applications, such as: - Construction: Architects and engineers use the concept of rhombus area to calculate the required materials for structures with rhombus-shaped components, such as roofs or decorative elements. - Geometry: Understanding the area of a rhombus helps in solving geometric problems and analyzing the properties of different shapes. - Art and Design: Artists and designers often incorporate rhombus-shaped patterns in their work, and knowing the area helps in creating balanced and visually appealing compositions.
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