Question

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In Exercise 4, find the surface area of the solid
formed by the net.

Answer 1

Exact Surface Area =
`480+32√(3)`

Approximate Surface Area = 535.425625842204

Round the approximate value however you need to

Units are in square centimeters.

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Work Shown:

You have the 160 portions correct since 20*8 = 160.

The other pieces are equilateral triangles, in which we use the formula

`A = (√(3))/(4)x^2`

where x is the side length of the triangle. Plug in x = 8 to get

`A = (√(3))/(4)x^2\\\\A = (√(3))/(4)8^2\\\\A = √(3)*(1)/(4)*64\\\\A = √(3)*16\\\\A = 16√(3)\\\\`

That's the exact area of one triangle, but we have two of them. Double the result to get
`2*16*√(3) = 32√(3)`

The total surface area is the sum of all the smaller areas

`160+160+160+32√(3) = 480+32√(3)`

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The exact surface area is
`480+32√(3)` square cm.

Using a calculator, you should get
`480+32√(3) \approx 535.425625842204`

Round this however you need to.