The Pythagorean theorem defines the relationship between the side lengths of a right triangle. The length of the hypotenuse squared (c²) is equal to the sum of the two perpendicular sides squared (a² + b²): c² = a² + b² or, solved for c, \(c = \sqrt{a + b}\)

The formula for area is πr². Radius is circle \( \frac{diameter}{2} \):

r = \( \frac{d}{2} \)
r = \( \frac{8}{2} \)
r = 4
a = πr²
a = π(4²)
a = 16π

The entire length of this line is represented by AD which is AB + BD:

AD = AB + BD

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 + 7b - 20 = 5b - 5
b² + 7b - 20 + 5 = 5b
b² + 7b - 5b - 15 = 0
b² + 2b - 15 = 0

Next, factor the quadratic equation:

b² + 2b - 15 = 0
(b - 3)(b + 5) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b - 3) or (b + 5) must equal zero:

If (b - 3) = 0, b must equal 3
If (b + 5) = 0, b must equal -5

So the solution is that b = 3 or -5

The area of a triangle is equal to ½ base x height:

a = ½bh
a = ½ x 9 x 9 = \( \frac{81}{2} \) = 40\(\frac{1}{2}\)