Question

How do you find the surface area for this shape?

Answer 1

Answer:

• total area is the total of the areas of each of the rectangular surfaces
• 67 units²

Step-by-step explanation:

Add up the surface areas of each of the 6 faces.

There are two top/bottom faces with the same area, two left/right faces with the same area, and two front/back faces with the same area. So you only need to figure the areas for 3 faces, then multiply that sum by 2. Of course the area of each rectangle is the product of its length and width. For length, width, and height dimensions L, W, and H, the total area is ...

A = 2(LW +WH +LH)

  = 2(LW +H(L+W)) . . . . . I like this form because there's one less multiplication

  = 2(5·4 + 1.5(5+4)) = 2(20 +13.5)

A = 67 . . . units²

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Comment on dimensions

It does not matter which number you use for length, width, or height. The problem is symmetrical that way, so any of the dimensions can be called any of those things. You need to use the same number consistently for height (for example) once you have made the choice of which is which.