To find the area of Mike's dilated triangle, we can follow these steps:
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Calculate the area of the original triangle: The area \( A \) of a triangle is given by the formula: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] For the original triangle:
- Base = 6 inches
- Height = 4 inches
So the area of the original triangle is: \[ A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
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Use the scale factor to find the area of the dilated triangle: The area of a shape scales by the square of the scale factor when dilated. In this case, the scale factor is 2.5. Therefore, the area of the dilated triangle can be calculated as: \[ \text{Area of dilated triangle} = \text{Area of original triangle} \times \text{(scale factor)}^2 \] \[ = 12 \times (2.5)^2 \] \[ = 12 \times 6.25 = 75 \text{ square inches} \]
Therefore, the area of Mike's dilated triangle is 75 square inches.