Answer: 48
Explanation:
If the base has a length of 12 and the perimeter is 32, then each of the legs are 10 inches.
If we construct the altitude from the vertex angle, we get two right triangles, each with a hypotenuse of 10 and a leg of 6.
By the Pythagorean theorem, the length of the altitude is 8.
This means the area of each triangle is 24, and thus the area of the entire triangle is 48.