To find the area of Mike's dilated triangle, we first need to calculate the area of the original triangle. The area \( A \) of a triangle can be calculated using the formula:
\[ A = \frac{1}{2} \times \text{base} \times \text{height} \]
Given that the original triangle has a height of 4 inches and a base of 6 inches, we can plug in these values:
\[ A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
Next, when the triangle is dilated by a scale factor of 2.5, both the base and height are multiplied by this factor. The new dimensions will be:
- New height: \( 4 \times 2.5 = 10 \) inches
- New base: \( 6 \times 2.5 = 15 \) inches
Now, we can find the area of the dilated triangle using the same area formula:
\[ A_{\text{dilated}} = \frac{1}{2} \times \text{new base} \times \text{new height} \]
Substituting in the new dimensions:
\[ A_{\text{dilated}} = \frac{1}{2} \times 15 \times 10 = \frac{1}{2} \times 150 = 75 \text{ square inches} \]
Thus, the area of Mike's dilated triangle is 75 square inches.