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

Find the area of rhombus if its vertices are (3,0),(4,5),(-1,4)and(-2,

1.	Find the area of rhombus if its vertices are (3,0),(4,5),(-1,4)and(-2,-1)taken in order.
Answer» Let A (3, 0), B (4, 5), C (-1, 4) and D (-2, -1){tex}AC = \\sqrt {{{( - 1 - 3)}^2} + {{(4 - 0)}^2}} = 4\\sqrt 2 {/tex}{tex}BD = \\sqrt {{{( - 2 - 4)}^2} + {{( - 1 - 5)}^2}} = \\sqrt {36 + 36} = 6\\sqrt 2 {/tex}Area of rhombus = {tex}\\frac{1}{2}{d_1} \\times {d_2}{/tex}{tex} = \\frac{1}{2}AC \\times BD{/tex}{tex} = \\frac{1}{2} \\times 4\\sqrt 2 \\times 6\\sqrt 2 = 24{/tex} Sq. unit.