Triangle with two sides given find the greatest area if the area is prime number

Question

A triangle has two sides of lengths 4 centimeters and 6 centimeters. Its area is n square centimeters, where n is a prime number. What is the greatest possible value of n? (A) 11 (B) 12 (C) 19 (D) 23 (E) 24

Answer 1

Hints:

1. Area of a triangle $A = \left|\frac{1}{2}ab\sin\theta\right|$ where $a, b$ are the lengths of two sides and $\theta$ is the angle between them.
2. $|\sin\theta| \le 1$
3. (B) is not a prime number