A trapezoid is a quadrilateral with one set of parallel 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 4 x 1) + (2 x 1 x 1) + (2 x 4 x 1)
sa = (8) + (2) + (8)
sa = 18

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

b² + 12b + 17 = 3b - 1
b² + 12b + 17 + 1 = 3b
b² + 12b - 3b + 18 = 0
b² + 9b + 18 = 0

Next, factor the quadratic equation:

b² + 9b + 18 = 0
(b + 3)(b + 6) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 3) or (b + 6) must equal zero:

If (b + 3) = 0, b must equal -3
If (b + 6) = 0, b must equal -6

So the solution is that b = -3 or -6

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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 = \( \sqrt{a} \) = \( \sqrt{49} \) = 7

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 = 7² + 7²
c² = 98
c = \( \sqrt{98} \) = \( \sqrt{49 x 2} \) = \( \sqrt{49} \) \( \sqrt{2} \)
c = 7\( \sqrt{2} \)