According to the Pythagorean theorem, the hypotenuse squared is equal to the sum of the two perpendicular sides squared:

c² = a² + b²
c² = 9² + 1²
c² = 81 + 1
c² = 82
c = \( \sqrt{82} \)

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(9 + 9)(4)
a = ½(18)(4)
a = ½(72) = \( \frac{72}{2} \)
a = 36

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 18 as well and sum (Inside, Outside) to equal -9. For this problem, those two numbers are -6 and -3. Then, plug these into a set of binomials using the square root of the First variable (y²):

y² - 9y + 18
y² + (-6 - 3)y + (-6 x -3)
(y - 6)(y - 3)

To solve this equation, replace the variables with the values given and then solve the now variable-free equation. (Remember order of operations, PEMDAS, Parentheses, Exponents, Multiplication/Division, Addition/Subtraction.)

-9a(a - y)
-9(-8)(-8 + 1)
-9(-8)(-7)
(72)(-7)
-504

To multiply monomials, multiply the coefficients (the numbers that come before the variables) of each term, add the exponents of like variables, and multiply the different variables together.

(9a)(5ab) - (6a²)(3b)
(9 x 5)(a x a x b) - (6 x 3)(a² x b)
(45)(a¹⁺¹ x b) - (18)(a²b)
45a²b - 18a²b
27a²b