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 = \( \sqrt{a} \) = \( \sqrt{16} \) = 4

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 = 4² + 4²
c² = 32
c = \( \sqrt{32} \) = \( \sqrt{16 x 2} \) = \( \sqrt{16} \) \( \sqrt{2} \)
c = 4\( \sqrt{2} \)

The volume of a cube is height x length x width:

v = h x l x w
v = 8 x 5 x 5
v = 200

You need to find the value of b so solve the first equation in terms of x:

b + x = 7
x = 7 - b

then substitute the result (7 - 1b) into the second equation:

-b + 6(7 - b) = -4
-b + (6 x 7) + (6 x -b) = -4
-b + 42 - 6b = -4
-b - 6b = -4 - 42
-7b = -46
b = \( \frac{-46}{-7} \)
b = 6\(\frac{4}{7}\)

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

The area of a parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 5 x 2
a = 10