Question

What is the area of the rhombus formed by (3, 0), (4, 5), (-1, 4) and (-2, -1) as vertices?

• A. 16 sq. units
• B. 32 sq. units
• C. 42 sq. units
• D. 24 sq. units

Answer 1

The correct option is D 24 sq. units

To find the area of rhombus ,the distance of two diagonals should be known

$BD=\sqrt{(-1-3{)}^2+(4-0{)}^2}\sqrt{16+16}=\sqrt{32}=4\sqrt{2}AC=\sqrt{(4+2{)}^2+(5+1{)}^2}=\sqrt{36+36}=\sqrt{72}=6\sqrt{2}$

Area of rhombu ABCD = $\frac{1}{2}\times$ product of diagonals.

$=\frac{1}{2}\times AC\times BD=\frac{1}{2}\times 4\sqrt{2}\times 6\sqrt{2}=24$ square unit.