Question

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

• A. 6
• B. 12
• C. 18
• D. 24

Answer 1

The correct option is D 24

Suppose A(3,0), B(4,5), C(-1,4), D(-2,-1) are the four consecutive sides of the rhombus such that AC and BD are the diagonals.
Area of rhombus is $\frac{1}{2}\times d1\times d2$, where d1 and d2 are the lengths of the two diagonals
$d1=AC=\sqrt{{\{3-(-1\left)\right\}}^2+{\{0-4\}}^2}=4\sqrt{2}$
$d2=BD=\sqrt{{\{4-(-2\left)\right\}}^2+{\{5-(-1\left)\right\}}^2}=6\sqrt{2}$
$Area=\frac{1}{2}\times d1\times d2=\frac{1}{2}\times 4\sqrt{2}\times 6\sqrt{2}=24$