Answer
$(a)$
$A=\frac{1}{2} ab \sin \theta$
$(b)$
$A=\sqrt{s(s-a)(s-b)(s-c)}$
Work Step by Step
$(a)$ For a triangle with sides $a$ and $b$ and angle $\theta$ between these sides, area is calculated by the formula :
$A=\frac{1}{2} ab \sin \theta$
$(b)$ If we know all of the sides of a triangle, we can calculate its area using Heron's Formula :
$A=\sqrt{s(s-a)(s-b)(s-c)}$
Where $s=\frac{1}{2}(a+b+c)$, that is semiperimeter.
