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

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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)]

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Solution

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

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

Length of diagonal BD =`sqrt([4-(-2)]^2+[5-(-1)]^2)`

`= sqrt(36+36) = 6sqrt2`

Therefore area of rhombus ABCD = `1/2xx4sqrt2xx6sqrt2`

= 24 square units

Concept: Section Formula
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APPEARS IN

NCERT Class 10 Maths
Chapter 7 Coordinate Geometry
Exercise 7.2 | Q 10 | Page 167

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