Question

Mike draws a triangle and dilates it by a scale factor of 2.5. I'd the triangles original dimensions are 4 high and 6 inches along its base, what is the area in square inches of mike's dilated triangle?

Answer 1

To find the area of the dilated triangle, we can use the following process:

1. **Calculate the area of the original triangle** using the formula for the area of a triangle:
\[
\text{Area} = \frac{1}{2} \times \text{base} \times \text{height}
\]
For Mike's original triangle:
- Height = 4 inches
- Base = 6 inches

So, the area of the original triangle is:
\[
\text{Area} = \frac{1}{2} \times 6 \times 4 = \frac{1}{2} \times 24 = 12 \text{ square inches}
\]

2. **Calculate the area of the dilated triangle**. The area of a triangle scales by the square of the scale factor when the triangle is dilated. Since the scale factor is 2.5, we will square it:
\[
\text{Scale Factor}^2 = (2.5)^2 = 6.25
\]

Now, multiply the area of the original triangle by this scale factor squared to get the area of the dilated triangle:
\[
\text{Area of dilated triangle} = \text{Area of original triangle} \times \text{Scale Factor}^2 = 12 \times 6.25 = 75 \text{ square inches}
\]

Thus, the area of Mike's dilated triangle is **75 square inches**.