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Two similar rectangular prism have corresponding sides that measure 5 feet and 6 feet.

If the surface area of a smaller prism is 525 square feet, what is the surface area of a larger prism?

Duplicate post-- already answered

To find the surface area of a larger prism, we need to understand the relationship between the dimensions of the two prisms and their corresponding surface areas.

Since the prisms are similar, their corresponding sides are proportional. This means that if the smaller prism has corresponding sides measuring 5 feet and 6 feet, the larger prism's sides are in the same ratio.

To scale up the dimensions of the smaller prism to find the dimensions of the larger prism, we need to determine the scaling factor. This can be found by dividing the corresponding sides of the larger prism by the corresponding sides of the smaller prism.

In this case, the larger prism's corresponding side is 6 feet. Dividing by the smaller prism's side of 5 feet, we get a scaling factor of 6/5.

To find the surface area of the larger prism, we can use the scaling factor to scale up the smaller prism's surface area. The relationship between the surface areas of similar prisms follows the square of the scaling factor.

Thus, to find the surface area of the larger prism, we multiply the surface area of the smaller prism by the square of the scaling factor: (525 square feet) * (6/5)^2.

Calculating this, we have (525 square feet) * (36/25), which simplifies to 756 square feet.

Therefore, the surface area of the larger prism is 756 square feet.