We have a right triangle with sides 12 cm, 15 cm and 19 cm.
The area of the triangle is half the product of the legs, as they represent the base and height of the triangle:
![A=(b\cdot h)/(2)=(12\cdot15)/(2)=6\cdot15=90\operatorname{cm}^2]()
NOTE: The legs are the shortest sides that form the right angle of the triangle.
Answer: the area of the triangle is 90 cm^2