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 parallelogram is equal to its length x width:

a = l x w
a = a x b
a = 6 x 8
a = 48

The formula for area is πr²:

a = πr²
a = π(5²)
a = 25π

For parallel lines with a transversal, the following relationships apply:

• angles in the same position on different parallel lines equal each other (a° = w°, b° = x°, c° = z°, d° = y°)
• alternate interior angles are equal (a° = z°, b° = y°, c° = w°, d° = x°)
• all acute angles (a° = c° = w° = z°) and all obtuse angles (b° = d° = x° = y°) equal each other
• same-side interior angles are supplementary and add up to 180° (e.g. a° + d° = 180°, d° + c° = 180°)

Applying these relationships starting with b° = 150, the value of c° is 30.

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 64 as well and sum (Inside, Outside) to equal -16. For this problem, those two numbers are -8 and -8. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 16y + 64
y² + (-8 - 8)y + (-8 x -8)
(y - 8)(y - 8)