Final answer:
If a shape has triple the dimensions of a similar shape, its area will be nine times greater because the area is proportional to the square of its dimensions.
Step-by-step explanation:
If a shape has triple the dimensions of a similar shape, it will have nine times the area. This is because the area of a shape is proportional to the square of its dimensions. Let's take an example to understand this concept:
Imagine a square with a side length of 4 inches. If we have a similar square with dimensions that are twice the original, the side length of the larger square would be: 4 inches × 2 = 8 inches. The area of the smaller square is 4 inches × 4 inches = 16 square inches, and the area of the larger square would be 8 inches × 8 inches = 64 square inches. Hence, the area of the larger square is four times the area of the smaller square. Extending this logic, if a shape has triple the dimensions, its side lengths would be multiplied by 3, and its area would be the square of the scale factor, i.e., 3² = nine times the area.