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

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(4 + 4)(3)
a = ½(8)(3)
a = ½(24) = \( \frac{24}{2} \)
a = 12

The first step to solve a quadratic expression that's not set to zero is to solve the equation so that it is set to zero:

y² - y + 0 = 2y - 2
y² - y + 0 + 2 = 2y
y² - y - 2y + 2 = 0
y² - 3y + 2 = 0

Next, factor the quadratic equation:

y² - 3y + 2 = 0
(y - 1)(y - 2) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (y - 1) or (y - 2) must equal zero:

If (y - 1) = 0, y must equal 1
If (y - 2) = 0, y must equal 2

So the solution is that y = 1 or 2

A monomial contains one term, a binomial contains two terms, and a polynomial contains more than two terms.

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\( \sqrt{2} \)