Answer
$A=\frac{1}{2} \times a \times b$ square inch.
Work Step by Step
By using the formula $A=\frac{1}{2} \times a \times b \times sin\gamma$ to calculate the area of the triangle, we can see that we have to maximize the $sin\gamma$.
The maximum is 1 where $\gamma = 90^{\circ}$
So the maximum area of the triangle is $A=\frac{1}{2} \times a \times b \times 1$.
