Question

Determine the total surface area of each right triangle-based prism

Answer 1

Answer:

• small prism: 630 m²
• large prism: 2520 m²

Step-by-step explanation:

The total surface area of the prism is the sum of the base area and the lateral area. The base area is made up of two right triangles, so will be the product of the triangle leg dimensions. The lateral area is made up of three rectangles whose width is that of the prism and whose equivalent length is the perimeter of the triangle base.

For the smaller prism, the area is ...

  (20 m)(21 m) +(3 m)(20 m + 21 m + 29 m) = 420 m² +210 m² = 630 m²

The larger prism is similar, with a scale factor of 2, so its area will be 2² = 4 times that of the smaller prism:

  4×630 m² = 2520 m²

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In summary, the total surface area of each prism is ...

• small prism: 630 m²
• large prism: 2520 m²