Question

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Answer 1

Answer:

Exact Surface Area = $480+32\sqrt{3}$

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

$A = \frac{\sqrt{3}}{4}x^2$

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

$A = \frac{\sqrt{3}}{4}x^2\\\\A = \frac{\sqrt{3}}{4}8^2\\\\A = \sqrt{3}*\frac{1}{4}*64\\\\A = \sqrt{3}*16\\\\A = 16\sqrt{3}$

That's the exact area of one triangle, but we have two of them. Double the result to get $2*16*\sqrt{3} = 32\sqrt{3}$

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

$160+160+160+32\sqrt{3} = 480+32\sqrt{3}$

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The exact surface area is $480+32\sqrt{3}$ square cm.

Using a calculator, you should get $480+32\sqrt{3} \approx 535.425625842204$

Round this however you need to.