Question

If the vertices of rhombus are (3, 0), (4, 5), (-1,4) and (-2, -1) taken in order then area of. rhombus is :

• A. 20 square units
• B. 24 square units
• C. 22 square units
• D. 26 square units

Answer 1

Answer: (B)

24 square units

Let $A(3,0),B(4,5),C(-1,4)$ and $D(-2,-1)$
We know that area of a rhombus $=\frac{1}{2}\times diagonal1\times diagonal2$
=> Area of the rhombus $=\frac{1}{2}\times \sqrt{{(-1-3)}^2+{(4-0)}^2}\times \sqrt{{(-2-4)}^2+{(-1-5)}^2}$
$=\frac{1}{2}\times \sqrt{32}\times \sqrt{72}=\frac{1}{2}\times 4\sqrt{2}\times 6\sqrt{2}=24squnits$