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 3) + (2 x 3 x 2) + (2 x 8 x 2)
sa = (48) + (12) + (32)
sa = 92

The perimeter of a triangle is the sum of the lengths of its sides:

p = x + y + z
p = 5cm + 15cm + 14cm = 34cm

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 = \( \sqrt{a} \) = \( \sqrt{81} \) = 9

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 = 9² + 9²
c² = 162
c = \( \sqrt{162} \) = \( \sqrt{81 x 2} \) = \( \sqrt{81} \) \( \sqrt{2} \)
c = 9\( \sqrt{2} \)

To solve this equation, repeatedly do the same thing to both sides of the equation until the variable is isolated on one side of the > sign and the answer on the other.

8c + 8 > \( \frac{c}{1} \)
1 x (8c + 8) > c
(1 x 8c) + (1 x 8) > c
8c + 8 > c
8c + 8 - c > 0
8c - c > -8
7c > -8
c > \( \frac{-8}{7} \)
c > -1\(\frac{1}{7}\)

The area of a trapezoid is one-half the sum of the lengths of the parallel sides multiplied by the height:

a = ½(b + d)(h)
a = ½(6 + 5)(4)
a = ½(11)(4)
a = ½(44) = \( \frac{44}{2} \)
a = 22