To find the area of the dilated triangle, we first need to determine the area of the original triangle using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle, the height is 4 inches, and the base is 6 inches. Plugging these values into the formula gives:
\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
Next, when we dilate the triangle by a scale factor of 2.5, the dimensions of the triangle will be multiplied by this scale factor. Specifically:
- The new height will be: \( 4 \times 2.5 = 10 \) inches
- The new base will be: \( 6 \times 2.5 = 15 \) inches
Now we can find the area of the dilated triangle using the same area formula:
\[ \text{Area} = \frac{1}{2} \times 15 \times 10 = \frac{1}{2} \times 150 = 75 \text{ square inches} \]
Thus, the area of Mike's dilated triangle is \( \boxed{75} \).