A triangle has sides $3x+1$, $x+2$, $x+3$ and an angle with a known cosine; find $x$ and area

Question

I'm having trouble with Question 10. I have figured out $x$, which is $2$. I'm not sure how I can find the area of the triangle. Please look at the attachment above.

Answer 1

If you have $x$, then you have all three side lengths. Now just apply Heron's formula.

Answer 2

HINT

By law of cosine we have

$$c^2 = a^2 + b^2-2ab\cos \theta$$

then we can find the area by

$$A=\frac12 ab\sin \theta$$