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 = \( \sqrt{a} \) = \( \sqrt{4} \) = 2

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 = 2² + 2²
c² = 8
c = \( \sqrt{8} \) = \( \sqrt{4 x 2} \) = \( \sqrt{4} \) \( \sqrt{2} \)
c = 2\( \sqrt{2} \)

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

-7c + y = -8
y = -8 + 7c

then substitute the result (-8 - -7c) into the second equation:

3c - 4(-8 + 7c) = -4
3c + (-4 x -8) + (-4 x 7c) = -4
3c + 32 - 28c = -4
3c - 28c = -4 - 32
-25c = -36
c = \( \frac{-36}{-25} \)
c = 1\(\frac{11}{25}\)

A parallelogram is a quadrilateral with two sets of parallel sides. Opposite sides (a = c, b = d) and angles (red = red, blue = blue) are equal. The area of a parallelogram is base x height and the perimeter is the sum of the lengths of all sides (a + b + c + d).

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(8 + 2)(2)
a = ½(10)(2)
a = ½(20) = \( \frac{20}{2} \)
a = 10

To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -36 as well and sum (Inside, Outside) to equal 0. For this problem, those two numbers are -6 and 6. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 36
y² + (-6 + 6)y + (-6 x 6)
(y - 6)(y + 6)