Final answer:
The area of triangle ABC is approximately 83.91 square units.
Step-by-step explanation:
To find the area of triangle ABC, we can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c is given by:
Area = sqrt(s(s-a)(s-b)(s-c)),
where s is the semiperimeter of the triangle, calculated as (a+b+c)/2.
In this case, a=6, b=7, and c=9. We can substitute these values into the formula to find the area:
Area = sqrt((6+7+9) * (6+7-9) * (6-7+9) * (-6+7+9))
= sqrt(22 * 4 * 8 * 10)
= sqrt(7040)
Therefore, the area of triangle ABC is approximately 83.91 square units.