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

r = \( \frac{d}{2} \)
r = \( \frac{6}{2} \)
r = 3
a = πr²
a = π(3²)
a = 9π

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 + 11b + 55 = -4b - 1
b² + 11b + 55 + 1 = -4b
b² + 11b + 4b + 56 = 0
b² + 15b + 56 = 0

Next, factor the quadratic equation:

b² + 15b + 56 = 0
(b + 7)(b + 8) = 0

For this expression to be true, the left side of the expression must equal zero. Therefore, either (b + 7) or (b + 8) must equal zero:

If (b + 7) = 0, b must equal -7
If (b + 8) = 0, b must equal -8

So the solution is that b = -7 or -8

An isosceles triangle has two sides of equal length. An equilateral triangle has three sides of equal length. In a right triangle, two sides meet at a right angle.

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 = \( \sqrt{a} \) = \( \sqrt{25} \) = 5

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 = 5² + 5²
c² = 50
c = \( \sqrt{50} \) = \( \sqrt{25 x 2} \) = \( \sqrt{25} \) \( \sqrt{2} \)
c = 5\( \sqrt{2} \)