Final answer:
To find the area of the enlargement, multiply the area of the original trapezium by 9.
Step-by-step explanation:
To find the area of the enlargement, we need to first find the area of the original trapezium. Since the area of the original trapezium is given as 6.3cm² and the enlargement is done with a scale factor of 3, we can use the formula for the area of a trapezium to calculate the dimensions of the original trapezium. Let's assume the dimensions of the original trapezium are b₁, b₂, and h.
Area of original trapezium = (1/2)(b₁ + b₂)h = 6.3cm²
Next, since the scale factor is 3, the dimensions of the enlarged trapezium will be 3 times the dimensions of the original trapezium. Let's call the dimensions of the enlarged trapezium B₁, B₂, and H.
Area of enlarged trapezium = (1/2)(B₁ + B₂)H
We can now use the fact that the dimensions of the enlarged trapezium are 3 times the dimensions of the original trapezium to rewrite the area of the enlarged trapezium equation in terms of the original trapezium dimensions:
Area of enlarged trapezium = (1/2)(3b₁ + 3b₂)(3h) = 9(1/2)(b₁ + b₂)h = 9 times the area of the original trapezium
Therefore, the area of the enlargement is 9 times the area of the original trapezium:
Area of enlargement = 9(6.3cm²) = 56.7cm²