Find the area of a rhombus if its vertises are (3,0),(4,5), (-1,4) and (-2,-1) taken in order.[Hint : Area of a rhombus=1/2( product of its diagonals)]
Answers
Answer:
- 24 sq.units
Step-by-step explanation:
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