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the scale factor of the larger of two similar rectangular prisms is 1/8. the surface area of the larger prism is 740 ft2. identify the surface area, rounded to the nearest tenth, of the smaller prism

Sagot :

sqdancefan

Answer:

  11.6 ft²

Step-by-step explanation:

We assume the 1/8 scale factor is the ratio of the linear dimensions of the smaller of the prisms to the larger. The ratio of areas will be the square of the ratio of the linear dimensions.

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The ratio of areas will be ...

  smaller area / larger area = (scale factor)²

  smaller area = (larger area)×(scale factor)² . . . multiply by the denominator

  smaller area = (740 ft²) × (1/8)² = 11.5625 ft² . . . use given values

The surface area of the smaller prism is about 11.6 square feet.

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