Geometry equations

Square Area

The area of a square is calculated as $A = s^{2}$, where $s$ is the side length.

Square Perimeter

The perimeter of a square is given by $P = 4s$.

Rectangle Area

The area of a rectangle is calculated as $A = l \times w$, where $l$ is the length and $w$ is the width.

Rectangle Perimeter

The perimeter of a rectangle is given by $P = 2l + 2w$.

Triangle Area

The area of a triangle is calculated as $A = \frac{1}{2}bh$, where $b$ is the base and $h$ is the height.

Triangle Perimeter

The perimeter of a triangle is the sum of all three sides: $P = a + b + c$.

Circle Area

The area of a circle is calculated as $A = \text{π} r^2$, where $r$ is the radius.

Circle Circumference

The circumference of a circle can be calculated as either $C = 2\text{π} r$ or $C = \text{π} d$, where $d$ is the diameter.

Parallelogram Area

The area of a parallelogram is calculated as $A = bh$, where $b$ is the base and $h$ is the height.

Parallelogram Perimeter

The perimeter of a parallelogram is given by $P = 2a + 2b$.

Trapezoid Area

The area of a trapezoid is calculated as $A = \frac{1}{2}h(b_1 + b_2)$, where $h$ is the height and $b_1$ and $b_2$ are the lengths of the parallel bases.

Trapezoid Perimeter

The perimeter of a trapezoid is the sum of all sides: $P = a + b + c + d$.

Cube Volume

The volume of a cube is calculated as $V = s^{3}$, where $s$ is the length of a side.

Cube Surface Area

The surface area of a cube is given by $SA = 6s^{2}$.

Rectangular Prism Volume

The volume of a rectangular prism is calculated as $V = l \times w \times h$.

Rectangular Prism Surface Area

The surface area of a rectangular prism is given by $SA = 2lw + 2lh + 2wh$.

Cylinder Volume

The volume of a cylinder is calculated as $V = \text{π} r^2 h$.

Cylinder Surface Area

The surface area of a cylinder is given by $SA = 2\text{π} r h + 2\text{π} r^2$.

Cone Volume

The volume of a cone is calculated as $V = \frac{1}{3}\text{π} r^2 h$.

Cone Surface Area

The surface area of a cone is given by $SA = \text{π} r(l + r)$, where $l$ is the slant height.

Sphere Volume

The volume of a sphere is calculated as $V = \frac{4}{3}\text{π} r^3$.

Sphere Surface Area

The surface area of a sphere is given by $SA = 4\text{π} r^2$.

Pythagorean Theorem

For right triangles, the Pythagorean theorem states that $a^2 + b^2 = c^2$ where $c$ is the hypotenuse.

Distance Formula

The distance between two points can be calculated using the formula $d = \text{√}((x_2 - x_1)^2 + (y_2 - y_1)^2)$.

Midpoint Formula

The midpoint between two points is given by $\text{Midpoint} = \bigg(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\bigg)$.

Slope of a Line

The slope of a line between two points is calculated as $m = \frac{y_2 - y_1}{x_2 - x_1}$.