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 = \( \sqrt{a} \) = \( \sqrt{9} \) = 3

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 = 3² + 3²
c² = 18
c = \( \sqrt{18} \) = \( \sqrt{9 x 2} \) = \( \sqrt{9} \) \( \sqrt{2} \)
c = 3\( \sqrt{2} \)

The circumference of a circle is the distance around its perimeter and equals π (approx. 3.14159) x diameter: c = π d. The area of a circle is π x (radius)² : a = π r².

To solve this equation, isolate the variable for which you are solving (b) on one side of the equation and put everything else on the other side.

8b - 8z = -b - 9z - 2
8b = -b - 9z - 2 + 8z
8b + b = -9z - 2 + 8z
9b = -z - 2
b = \( \frac{-z - 2}{9} \)
b = \( \frac{-z}{9} \) + \( \frac{-2}{9} \)
b = -\(\frac{1}{9}\)z - \(\frac{2}{9}\)

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 2) + (2 x 2 x 7) + (2 x 8 x 7)
sa = (32) + (28) + (112)
sa = 172

A trapezoid is a quadrilateral with one set of parallel sides.