Marisol draws a triangle with a 4-inch base and 6-inch height. She dilates the triangle by a scale factor of 1.5. Compare the areas of the dilated triangle and the original triangle. Use a decimal response if necessary.
The area of a triangle is given by the formula:
Area = (base * height) / 2
For the original triangle, the base is 4 inches and the height is 6 inches, so the area is:
Area_original = (4 * 6) / 2 = 12 square inches
To find the area of the dilated triangle, we multiply the original area by the square of the scale factor. In this case, the scale factor is 1.5, so:
Area_dilated = (1.5^2) * Area_original = 2.25 * 12 = 27 square inches
Therefore, the area of the dilated triangle is 27 square inches.