The adjacent sides of a parallelogram are 12cm and 14cm and angle between them is 60°. What is the area of the parallelogram?

A \(168\sqrt 3\ c{m^2}\)

B \(84\sqrt 3\ c{m^2}\)

C \(2/2\ c{m^2}\)

D \(324\sqrt 2\)

E None of these

Correct Answer: Option B

We know that :-

Formula :-

(i) Area of a parallelogram = base × height

(ii) Area of a parallelogram = product of two adjacent sides × sine of angle between them

From formula (ii) we get –

⇒ Area of the required parallelogram = 12 × 14 × sin 60° cm²

\(\eqalign{ & = 168 \times {{\sqrt 3 } \over 2}\ c{m^2} \cr & = 84\sqrt 3\ c{m^2} \cr}\)