Find the area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (- 2, - 1) taken in order. [Hint: Area of a rhombus =1/2 × (product of its diagonals)]

Solution:

A rhombus has all sides of equal length and opposite sides are parallel.

Let A(3, 0), B(4, 5), C(- 1, 4) and D(- 2, - 1) be the vertices of a rhombus ABCD.

Also, Area of a rhombus =1/2 × (product of its diagonals)

Hence we will calculate the values of the diagonals AC and BD.

We know that the distance between the two points is given by the distance formula,

Distance formula = √( x₂ ^_- x₁ )² + (y₂ - y₁)² 

Therefore, distance between A (3, 0) and C (- 1, 4) is given by

Length of diagonal AC =√ [3 - (-1)]² + [0 - 4]²

= √(16 + 16)

= 4√2 

The distance between B (4, 5) and D (- 2, - 1) is given by

Length of diagonal BD = √[4 - (-2)]² + [5 - (-1)]²

= √(36 + 36)

= 6√2

Area of the rhombus ABCD = 1/2 × (Product of lengths of diagonals) = 1/2 × AC × BD

Therefore, the area of the rhombus ABCD = 1/2 × 4√2 × 6√2 square units

= 24 square units

☛ Check: NCERT Solutions for Class 10 Maths Chapter 7

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Video Solution:

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (- 2, - 1) taken in order

NCERT Class 10 Maths Solutions  Chapter 7 Exercise 7.2 Question 10 

Summary:

The area of a rhombus if its vertices are (3, 0), (4, 5), (- 1, 4) and (- 2, - 1) taken in order is 24 square units.

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☛ Related Questions:

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