To find the area of a triangle, we use the formula:
Area = 1/2(base * height)
From the problem, we know that the base of the triangle is 6 inches and the height is 5 inches.
Substitute these values into the formula:
Area = 1/2(6 inches * 5 inches) 
Area = 1/2 * 30 square inches 
After performing the multiplication, our final area is 15 square inches. 
Therefore, the area of the triangle is 15.0 square inches.