Answer
Fill the blanks with
... $\displaystyle \frac{1}{2}ab\sin\theta$ ... $14$
Work Step by Step
Book references: p.498, p.483.
A triangle described as in the problem text has area
$ A=\displaystyle \frac{1}{2}ab\sin\theta$
For $30^{o}$, one of the special angles,
for which we have a table of trigonometric ratios (p.483),
$\displaystyle \sin 30^{o}=\frac{1}{2}$.
So$, A=\displaystyle \frac{1}{2}\cdot 4\cdot 7=14$
Fill the blanks with
... $\displaystyle \frac{1}{2}ab\sin\theta$ ... $14$
