To find the area of the dilated triangle, we first calculate the area of the original triangle and then apply the effect of the dilation.
The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle with a base of 6 inches and a height of 4 inches, the area is:
\[ A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
When a triangle is dilated by a scale factor \( k \), the area of the triangle is multiplied by \( k^2 \). Here, the scale factor is 2.5.
Calculating \( k^2 \):
\[ k^2 = (2.5)^2 = 6.25 \]
Now, we can find the area of the dilated triangle:
\[ \text{Area of dilated triangle} = \text{Area of original triangle} \times k^2 = 12 \times 6.25 = 75 \text{ square inches} \]
Thus, the area of Mike's dilated triangle is 75 square inches.