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Solution - Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order. - CBSE Class 10 - Mathematics

ConceptSection Formula

Question

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

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

Is there an error in this question or solution?

APPEARS IN

 NCERT Mathematics Textbook for Class 10 (with solutions)
Chapter 7: Coordinate Geometry
Q: 10 | Page no. 167

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Reference Material

Solution for question: Find the area of a rhombus if its vertices are (3, 0), (4, 5), (− 1, 4) and (− 2, −1) taken in order. concept: Section Formula. For the course CBSE
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