Using the hint that the ratio of surface areas is the scale factor squared, the surface area of prism 1 is 36 square cm
How to determine the surface area prism 1 using the hint that the ratio of surface areas is the scale factor squared?
From the figure, we have the following parameters
Prism 1 = 3 cm
Prism 2 = 8 cm
Calculate the scale ratio of dilation from prism 2 to prism 1 using the following equation
Scale ratio = Prism 1/Prism 2
Substitute the known values in the above equation
Scale ratio = 3m/8m
This gives
Scale ratio = 0.375
The surface area of prism 1 is then calculated using the following equation
Area of prism 2 = Scale ratio^2 * Area of prism 1
Substitute the known values in the above equation
Area of prism 2 = 0.375^2 * 256 square cm
Evaluate the product
Area of prism 2 = 36 square cm
Hence, the surface area of prism 1 is 36 square cm
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