PLZ HELP, DONT UNDERSTAND THIS​

9514 1404 393

  b)  800 cm²

Step-by-step explanation:

The surface area of the figure is the sum of the areas of each of the 6 faces. Three of the faces are shown. Because the figure is presumed to be a cuboid, the three faces not shown are identical in area to those that are.

Each face is a rectangle. As such, its area is the product of its dimension (length and width).

The front face has dimensions 10 in by 10 in. Its area is (10 in)·(10 in) = 100 in².

The top face has dimensions 10 in by 15 in. Its area is (10 in)·(15 in) = 150 in².

The right-side face has the same dimensions as the top face. Its area is also 150 in².

The sum of the areas of the three faces you can see is ...

  100 in² +150 in² + 150 in² = 400 in²

The three faces you cannot see have the same area, so the total surface area of this figure is ...

  SA = 2(400 in²) = 800 in² . . . . matches choice B

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The formula for this can be written a couple of different ways. One that matches what we did above is ...

  SA = 2(LW +WH +LH) . . . . where L, W, H are the length, width, and height

The formula is symmetrical with respect to L, W, and H, so it does not matter which number you assign to which letter. The only thing that matters is that the same letter always represents the same number.

The above formula requires 4 multiplications and 2 additions. It can be reduced to one that requires 3 multiplications and 2 additions by combining a couple of the terms. I like this formula because it is slightly less work.

  SA = 2(LW +H(L +W))