To find the area of the dilated triangle, we first need to calculate the area of the original triangle. The area \( A \) of a triangle can be found 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 the triangle is dilated by a scale factor of 2.5, the dimensions of the triangle are multiplied by 2.5. Therefore, the new base and height will be:
\[ \text{New base} = 6 \times 2.5 = 15 \text{ inches} \] \[ \text{New height} = 4 \times 2.5 = 10 \text{ inches} \]
Now, we can calculate the area of the dilated triangle using the same area formula:
\[ A' = \frac{1}{2} \times \text{new base} \times \text{new height} = \frac{1}{2} \times 15 \times 10 = \frac{1}{2} \times 150 = 75 \text{ square inches} \]
Thus, the area of Mike's dilated triangle is:
\[ \boxed{75} \text{ square inches} \]
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