Answer:
19.5 in²
Step-by-step explanation:
A applicable formula for the area of the smaller triangle is ...
A = (1/2)ab·sin(C) . . . . where a, b are the given sides and C is the angle between them.
The side lengths are 3 in and 13 in, so the area is ...
A = (1/2)(3 in)(13 in)sin(C) = (19.5 in²)sin(C)
The sine function is a maximum at C=90°, at which angle it has the value 1. So, the maximum area is that of a right triangle of sides lengths 3 and 13 inches.
The maximum area is 19.5 in².
