Answer
$18.7 \text{cm}^2 $
Work Step by Step
When the two sides let's say a and b and the angle C are given, then the area $\bf{A}$ can be calculated as:
$A=\dfrac{1}{2} ab \sin \text{C}$
From the given figure, we have: $ a= 8 \ \text{cm}; b = 6 \ \text{cm} ; C= 51^{\circ}$
$A=\dfrac{1}{2} (8) (6) \sin 51^{\circ} \approx 18.7 \text{cm}^2 $
