Question

Find the area of a rhombus if the vertices are A(4,5),B(-2,-1),C(3,0) and D(-1,4)​

Answer 1

area of rhombus =1/2(diagonal1 x diagonal 2)

Answer 2

Solution :-

Since ABCD is a rhombus . Length of its two diagonals is AC and BD .

So, using distance formula we get,

→ AC = √[(x1 - x2)² + (y1 - y2)²] = √[(4 - 3)² + (5 - 0)²] = √(1² + 5²) = √(1 + 25) = √26 units

→ BD = √[(x1 - x2)² + (y1 - y2)²] = √[(-2 + 1)² + (-1 - 4)²] = √{(-1)² + (-5)²} = √(1 + 25) = √26 units

then,

→ Area of Rhombus = (1/2) * Diagonal 1 * Diagonal 2 .

→ Area of Rhombus ABCD = (1/2) * AC * BD

→ Area of Rhombus ABCD = (1/2) * √26 * √26

→ Area of Rhombus ABCD = (1/2) * 26

→ Area of Rhombus ABCD = 13 units² (Ans.)

Hence, the area of rhombus ABCD will be 13 units² .

Learn more :-

prove that the mid point of the line joining points (-5,12) and (-1,12) is a point of trisection of the line joining the...

https://brainly.in/question/15118408

in what ratio is tge line joining the points (9, 2) and (-3, - 2 ) divided by the y axis? also find the coordinate of th...

https://brainly.in/question/15022879

find the equation of the straight line which passes through the point 4,3 and parallel to line 3x +4y=7

https://brainly.in/question/15527182