To find the area of Mike's dilated triangle, we first need to calculate the area of the original triangle and then apply the scale factor to find the area of the dilated triangle.
-
Calculate the area of the original triangle: The formula for the area \( A \) of a triangle is given by: \[ A = \frac{1}{2} \times \text{base} \times \text{height} \] For the original triangle: \[ \text{base} = 6 \text{ inches}, \quad \text{height} = 4 \text{ inches} \] \[ A = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
-
Apply the dilation scale factor: When a figure is dilated, its area changes by the square of the scale factor. Here, the scale factor is \( 2.5 \), so we calculate the new area: \[ \text{New Area} = \text{Original Area} \times \text{(Scale Factor)}^2 \] \[ \text{New Area} = 12 \times (2.5)^2 \] \[ (2.5)^2 = 6.25 \] \[ \text{New Area} = 12 \times 6.25 = 75 \text{ square inches} \]
Therefore, the area of Mike's dilated triangle is 75 square inches.
2 answers