To find the area of Mike's dilated triangle, we first calculate the area of the original triangle using the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
The original triangle has a height of 4 inches and a base of 6 inches. Therefore, the area of the original triangle is:
\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
Since the triangle is dilated by a scale factor of 2.5, the dimensions of the triangle after dilation will be multiplied by this scale factor. The new dimensions are:
- Height: \(4 \times 2.5 = 10\) inches
- Base: \(6 \times 2.5 = 15\) inches
Now, we calculate the area of the dilated triangle using the same area formula:
\[ \text{Area}{\text{dilated}} = \frac{1}{2} \times \text{base}{\text{dilated}} \times \text{height}_{\text{dilated}} = \frac{1}{2} \times 15 \times 10 \]
Calculating this gives:
\[ \text{Area}_{\text{dilated}} = \frac{1}{2} \times 150 = 75 \text{ square inches} \]
Thus, the area of Mike's dilated triangle is 75 square inches.
The correct response is: 75.