Question

It is given that a rhombus is obtained by joining the midpoints of the pairs of opposite sides of a rectangle. What is the area of the rhombus so obtained if the length and breadth of the rectangle are 8 cm and 6 cm respectively?

• A. $48{\text{cm}}^2$
• B. $24{\text{cm}}^2$
• C. $12{\text{cm}}^2$
• D. $28{\text{cm}}^2$

Answer 1

The correct option is B $24{\text{cm}}^2$

The length of the diagonals of the rhombus will be equal to the length and breadth of the rectangle.
Thus, AD = BC = PR = 8 cm and AB = CD = QS = 6 cm.

Area of a rhombus is equal to half the product of its diagonals.
Area of ABCD = $\frac{1}{2}\times PR\times QS$
= $\frac{1}{2}\times 8\times 6$
= $24{\text{cm}}^2$