A rhombus is a parallelogram with four equal-length sides. A square is a rectangle with four equal-length sides.

The surface area of a cube is (2 x length x width) + (2 x width x height) + (2 x length x height):

sa = 2lw + 2wh + 2lh
sa = (2 x 8 x 8) + (2 x 8 x 2) + (2 x 8 x 2)
sa = (128) + (32) + (32)
sa = 192

The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is 1. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 4) and (2, -2) so the slope becomes:

Plugging these values into the slope-intercept equation:

y = -1\(\frac{1}{2}\)x + 1

To find the diagonal we need to know the length of one of the square's sides. We know the area and the area of a square is the length of one side squared:

a = s²

so the length of one side of the square is:

s = \( \sqrt{a} \) = \( \sqrt{1} \) = 1

The Pythagorean theorem defines the square of the hypotenuse (diagonal) of a triangle with a right angle as the sum of the squares of the other two sides:

c² = a² + b²
c² = 1² + 1²
c² = 2
c = \( \sqrt{2} \)

The first step to solve a quadratic equation that's set to zero is to factor the quadratic equation:

b² - 81 = 0
(b - 9)(b + 9) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 9) or (b + 9) must equal zero:

If (b - 9) = 0, b must equal 9
If (b + 9) = 0, b must equal -9

So the solution is that b = 9 or -9