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

a = l x w
a = a x b
a = 6 x 2
a = 12

The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

You need to find the value of a so solve the first equation in terms of y:

-4a + y = 2
y = 2 + 4a

then substitute the result (2 - -4a) into the second equation:

-3a + 5(2 + 4a) = -2
-3a + (5 x 2) + (5 x 4a) = -2
-3a + 10 + 20a = -2
-3a + 20a = -2 - 10
17a = -12
a = \( \frac{-12}{17} \)
a = -\(\frac{12}{17}\)

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\( \sqrt{2} \)

A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.