Find the area of a rhombus if its vertices are (3, 0), (4, 5), (– 1, 4) and (– 2, – 1) taken inorder. [Hint: Area of a rhombus (product of its diagonals)]

Question

Find the area of a rhombus if its vertices are (3, 0), (4, 5), (&#x2013; 1, 4) and (&#x2013; 2, &#x2013; 1) taken inorder. [Hint: Area of a rhombus (product of its diagonals)]

Philoid · Accepted Answer

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 = [(3 + 1)² + (0 – 4)²]^1/2

=

Length of diagonal BD = [(4 + 2)² + (5+ 1)²]^1/2

=

= 6

Therefore,

Area of rhombus ABCD = * * 6

= 24 square units