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(6 + 9)(2)
a = ½(15)(2)
a = ½(30) = \( \frac{30}{2} \)
a = 15

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:

b² + b - 8 = 4b + 2
b² + b - 8 - 2 = 4b
b² + b - 4b - 10 = 0
b² - 3b - 10 = 0

Next, factor the quadratic equation:

b² - 3b - 10 = 0
(b + 2)(b - 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 2) or (b - 5) must equal zero:

If (b + 2) = 0, b must equal -2
If (b - 5) = 0, b must equal 5

So the solution is that b = -2 or 5

A triangle is a three-sided polygon. It has three interior angles that add up to 180° (a + b + c = 180°). An exterior angle of a triangle is equal to the sum of the two interior angles that are opposite (d = b + c). The perimeter of a triangle is equal to the sum of the lengths of its three sides, the height of a triangle is equal to the length from the base to the opposite vertex (angle) and the area equals one-half triangle base x height: a = ½ base x height.

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 14 as well and sum (Inside, Outside) to equal -9. For this problem, those two numbers are -7 and -2. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 9y + 14
y² + (-7 - 2)y + (-7 x -2)
(y - 7)(y - 2)