Answer:
The correct option is;
She forgot to square the scale factor
Step-by-step explanation:
The parameters given are;
Dimensions of large rectangle;
Base = 30 cm
Height = 25.5
Dimensions of the small rectangle;
Base = b
Height = a
The formula to find the area of scaled dimension (small triangle) is given as follows;
Area of small triangle = (Scale factor)² × Original (or actual) area
Whereby the area, A, of a triangle is given as follows;
![A = \dfrac{1}{2} \times Base \times Height](https://tex.z-dn.net/?f=A%20%3D%20%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20Base%20%5Ctimes%20Height)
The smaller triangle area,
, should therefore be given as follows;
![A_{small} =\dfrac{1}{2} \times Base \times Height \times (scale \ factor)^2](https://tex.z-dn.net/?f=A_%7Bsmall%7D%20%3D%5Cdfrac%7B1%7D%7B2%7D%20%5Ctimes%20Base%20%5Ctimes%20Height%20%5Ctimes%20%20%28scale%20%5C%20factor%29%5E2)
Plugging in the values, we have;
![A_{small} = \left (\dfrac{1}{2} \right )\times (25.5) \times (30)\times \left (\dfrac{1}{5} \right )^2 = 15.3 \ cm^2](https://tex.z-dn.net/?f=A_%7Bsmall%7D%20%3D%20%5Cleft%20%28%5Cdfrac%7B1%7D%7B2%7D%20%20%5Cright%20%29%5Ctimes%20%2825.5%29%20%5Ctimes%20%2830%29%5Ctimes%20%20%5Cleft%20%28%5Cdfrac%7B1%7D%7B5%7D%20%20%5Cright%20%29%5E2%20%3D%2015.3%20%5C%20cm%5E2)
However, from the question, we have;
(1/2)(25.5)(30)(1/5) = 76.5 cm²
Therefore, the correct option is that she forgot to square the scale factor.