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Area of a rhombus = 1/2 product of _________.

Solution:

A rhombus is a parallelogram with the following properties:

1) All sides equal

2) Diagonals which are equal and bisect each other at right angles

3) Opposite angles are equal

Area of a rhombus = 1/2 product of _________

The area of the rhombus is equal to the sum of all the four triangles △AOB, △BOC, △DOC and △AOD. Their sum can be expressed as :

Area of rhombus(A) = 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2) + 1/2 × (x/2) × (y/2)

Area of Rhombus(A) = 4 × (xy/8) = xy/2

The length of one diagonal = x

The length of the other diagonal = y

Since the Area of the Rhombus(A) as calculated above is xy/2 we can state:

Area of rhombus = 1/2 × (Product of the diagonals x and y)

Therefore,

The area of the rhombus is a parallelogram with all sides equal and its area is equal to the half of the product of its diagonals.

✦ Try This: If the area of the rhombus is 32cm² and one diagonal is 8 cm then the the length of the other diagonal is ___________.

The area of the rhombus is half the product of its diagonals and is mathematically stated as:

Area of Rhombus = (1/2) × D₁ × D₂

Where D₁ and D₂ are the two diagonals of the rhombus.

Area of the Rhombus(A) = 32 cm²

Length of one diagonal = 8 cm

Therefore the length of the other diagonal is equal:

A = 32 = (1/2) × D₁ × D₂

(1/2) × (8) × D₂ = 32

D₂ = 8 cm

The length of the other diagonal is 8cm.

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 46

Summary:

Area of a rhombus = 1/2 product of its diagonals

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