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# In the cube above, the length of line segment AB is

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In the cube above, the length of line segment AB is [#permalink]  30 Jul 2017, 11:06
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In the cube above, the length of line segment AB is 8. The surface area of the cube equals what?

[Reveal] Spoiler: OA
192

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Kudos [?]: 450 [1] , given: 3

Re: In the cube above, the length of line segment AB is [#permalink]  30 Jul 2017, 17:59
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Carcass wrote:
Attachment:
shot3.jpg

In the cube above, the length of line segment AB is 8. The surface area of the cube equals what?

[Reveal] Spoiler: OA
192

Each face of the cube is a SQUARE, and there are 6 faces on a cube.

Imagine a square with sides of length x and a diagonal with length 8
The diagonal divides the square into to right triangles.
Focus on one of the right triangles.
The two legs have length x, and the hypotenuse (aka diagonal) has length 8
Applying the Pythagorean Theorem, we can write: x² + x² = 8²
Simplify: 2x² = 64
Divide each side by 2 to get: x² = 32

IMPORTANT: we need not go any further and solve for x.
Well, the question asks us to find the surface area of the cube.
Since each face of the cube is a SQUARE, we need to find the area of each of the 6 identical squares.
Area of a square = (base)(height) = (x)(x) =
Hey, we already know that x² = 32
So, the area of each of the cube's 6 squares is 32
So, the total surface area = (6)(32) = 192

Cheers,
Brent
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Brent Hanneson – Founder of greenlighttestprep.com

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Re: In the cube above, the length of line segment AB is   [#permalink] 30 Jul 2017, 17:59
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