The formula for the area of a circle is: \[ A = \pi r^2 \] where \( r \) is the radius of the circle.

The perimeter of a rectangle is calculated as: \[ P = 2l + 2w \] where \( l \) is the length and \( w \) is the width of the rectangle.

The Pythagorean Theorem states that in a right triangle: \[ a^2 + b^2 = c^2 \] where \( a \) and \( b \) are the lengths of the legs and \( c \) is the length of the hypotenuse.

The area of a triangle is given by: \[ A = \frac{1}{2} \cdot b \cdot h \] where \( b \) is the base and \( h \) is the height of the triangle.

The sum of the interior angles of a polygon with \( n \) sides is: \[ S = 180^\circ \times (n - 2) \]

The volume of a cylinder is calculated as: \[ V = \pi r^2 h \] where \( r \) is the radius of the base and \( h \) is the height of the cylinder.

The distance between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

The surface area of a sphere is given by: \[ A = 4\pi r^2 \] where \( r \) is the radius of the sphere.

The equation of a circle with center \( (h, k) \) and radius \( r \) is: \[ (x - h)^2 + (y - k)^2 = r^2 \]

The volume of a cone is calculated as: \[ V = \frac{1}{3} \pi r^2 h \] where \( r \) is the radius of the base and \( h \) is the height of the cone.