# 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.

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

Distance formula = √( x_{2 - }x_{1 })^{2} + (y_{2} - y_{1})^{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

Therefore, 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 x (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

**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:

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

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