Question

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

• A. $12$ sq. units
• B. $24$ sq. units
• C. $36$ sq. units
• D. $48$ sq. units

Answer 1

The correct option is B $24$ sq. units

Given, $A(3,0),B(4,5),C(-1,4)$ and $D(-2,-1)$

Here, $AC=\sqrt{(-1,-3{)}^2+(4-0{)}^2}=\sqrt{(-4{)}^2+4^2}$
$=\sqrt{16+16}=4\sqrt{2}$ units

$BD=\sqrt{(-2,-4{)}^2+(-1-5{)}^2}=\sqrt{(-6{)}^2+(-6{)}^2}$
$=\sqrt{36+36}=6\sqrt{2}$ units

Since, Area of rhombus $=\frac{1}{2}$ (product of its diagonals)
$=\frac{1}{2}\times 4\sqrt{2}\times 6\sqrt{2}$ sq. units $=24$ sq. units