## Elementary Geometry for College Students (7th Edition)

$A=\frac{1}{2} \times a \times b$ square inch.
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 $A=\frac{1}{2} \times a \times b \times 1$.