Question

Consider a quadrilateral ABCD with AC=12 cm and BD=10 cm with the following characteristics:
(i) Opposite angles are equal and parallel.
(ii) All sides are equal.
(iii) Diagonals bisect each other at right angles.
What is the area of ABCD?

• A. $30{\text{cm}}^2$
• B. $45{\text{cm}}^2$
• C. $60{\text{cm}}^2$
• D. $120{\text{cm}}^2$

Answer 1

The correct option is C $60{\text{cm}}^2$

From the given conditions, it is clear that the given quadrilateral is a rhombus.
Area of a rhombus=$\frac{1}{2}\times$ product of diagonals
$⟹$Area of ABCD=$\frac{1}{2}\times AC\times BD$
$=\frac{1}{2}\times 12\times 10$
$=60{\text{cm}}^2$