Final answer:
The area of a triangle depends on knowing which sides are the base and height. The larger square's area Marta has is four times the smaller one's due to the squared scale factor. For scale models, unit scales are used to convert real-world measurements proportionally.
Step-by-step explanation:
The surface area of a triangle can be calculated using the formula 1/2 × base × height. However, the question provides three measurements without clarification on which is the base or height. Assuming the longest side is the base, and one of the other measurements is the height, the area would be either (1/2 × 10 3/4 inches × 5 1/2 inches) or (1/2 × 8 inches × 5 1/2 inches), depending on which you take as height. The student needs to identify the base and height accurately to proceed.
Moving on to the examples provided, Marta has two squares. The larger square's area is four times that of the smaller square because the area is a function of the square of the side length. This is a result of the scale factor which at a factor of 2, increases the area by a factor of 2² (4).
Regarding the rectangular fish pond example, it illustrates how to use a unit scale to calculate dimensions for scale models. The ratio provided (1/2 inch = 5 feet) helps in scaling down real-world measurements to create accurate models or drawings.