Carcass wrote:
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In the cube above, the length of line segment AB is 8. The surface area of the cube equals what?
enter your valueEach 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 = 32IMPORTANT: we need not go any further and solve for x.
Why not you ask?
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) =
x²Hey, we already know that
x² = 32So, the area of each of the cube's 6 squares is
32 So, the total surface area = (6)(
32) =
192Cheers,
Brent
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Brent Hanneson - founder of Greenlight Test Prep