To find the area of Mike's dilated triangle, we first need to calculate the area of the original triangle.
The formula for the area of a triangle is:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]
For the original triangle:
- Base = 6 inches
- Height = 4 inches
Plugging in these values:
\[ \text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches} \]
Now, when Mike dilates the triangle by a scale factor of 2.5, the dimensions of the triangle will increase by this scale factor.
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:
\[ \text{Dilated Area} = \frac{1}{2} \times \text{new base} \times \text{new height} = \frac{1}{2} \times 15 \times 10 \]
Calculating this:
\[ \text{Dilated Area} = \frac{1}{2} \times 150 = 75 \text{ square inches} \]
Thus, the area of Mike’s dilated triangle is 75 square inches.
The correct response is:
75
1 answer