Question

In the quadrilateral ABCD, AC = 7 cm, BD = 8 cm and $\angle AXD={60}^{\circ }$. Find the area of ABCD.

• A. $28c{m}^2$
• B. $28\sqrt{3}c{m}^2$
• C. $14\sqrt{3}c{m}^2$
• D. $14c{m}^2$

Answer 1

The correct option is C $14\sqrt{3}c{m}^2$

Area $=\frac{1}{2}\times AC\times BD\times sin\angle AXD$
$=\frac{1}{2}\times 7\times 8\times sin{60}^{\circ }$
$=\frac{1}{2}\times 7\times 8\times \frac{\sqrt{3}}{2}=14\sqrt{3}c{m}^2$