Question

Area of a rhombus if its vertices are (3, 0), (4, 5), (-1, 4) and (-2, -1) taken in order is

• A. 24. sq. units
• B. 36 sq. units
• C. 48 sq. units
• D. 48$\sqrt{2}$ sq. units

Answer 1

Answer: (A)

24. sq. units

Let A(3,0), B(4,5), C(-1,4), D(-2,-1) be vertices of rhombus where AC and BD are diagonals of rhombus.
Use Distance formula to calculate Length of diagonals.
i.e., AC = $\sqrt{(}(3-(-1){)}^2+(0-4{)}^2)=4\sqrt{2}$
Similarly calculate for BD i.e.,
length of BD = $6\sqrt{2}$
Therefore, Area of Rhombus = BDXAC/2
Therefore,
Area of Rhombus = $24sq.units$