Admin 12 Jun 2026 17:36

admin #general

Geometry Formulas List

Geometry is a branch of mathematics that deals with shapes, sizes, the relative position of figures, and the properties of space. It is divided into two main categories: plane geometry (2D shapes) and solid geometry (3D shapes). Whether you are a student, a teacher, or a professional, having a quick reference guide for geometry formulas is essential for solving problems involving perimeter, area, volume, and surface area.

Common Variables Used

Before diving into the specific formulas, it is helpful to understand the common variables used in these equations:

$A$: Area
$P$: Perimeter
$C$: Circumference
$V$: Volume
$SA$: Surface Area
$l$: Length
$w$: Width
$h$: Height
$r$: Radius
$b$: Base
$s$: Side
$\pi$: Pi (approximately 3.14159)

2-Dimensional Geometry (Plane Shapes)

Plane geometry deals with flat shapes that can be drawn on a piece of paper. The primary measurements are perimeter (the distance around the shape) and area (the region occupied by the shape).

Rectangle

Perimeter: $P = 2(l + w)$

Area: $A = l \times w$

Where $l$ is length and $w$ is width.

Square

Perimeter: $P = 4s$

Area: $A = s^2$

Where $s$ is the length of one side.

Triangle

Perimeter: $P = a + b + c$

Area: $A = \frac{1}{2} \times b \times h$

Where $a, b, c$ are the lengths of the sides, $b$ is the base, and $h$ is the height.

Right Triangle

Pythagorean Theorem: $a^2 + b^2 = c^2$

Area: $A = \frac{1}{2} \times a \times b$

Where $a$ and $b$ are the legs (height and base) and $c$ is the hypotenuse.

Circle

Circumference: $C = 2\pi r$ or $C = \pi d$

Area: $A = \pi r^2$

Where $r$ is the radius and $d$ is the diameter ($d = 2r$).

Trapezoid

Perimeter: $P = a + b + c + d$

Area: $A = \frac{1}{2}(b_1 + b_2) \times h$

Where $b_1$ and $b_2$ are the lengths of the parallel bases, $h$ is the height, and $a, c$ are the non-parallel sides.

Parallelogram

Perimeter: $P = 2(a + b)$

Area: $A = b \times h$

Where $a$ and $b$ are the lengths of adjacent sides, and $h$ is the vertical height.

3-Dimensional Geometry (Solid Shapes)

Solid geometry deals with three-dimensional objects. The primary measurements are volume (the space inside the shape) and surface area (the total area of the outer surface).

Cube

Volume: $V = s^3$

Surface Area: $SA = 6s^2$

Where $s$ is the length of one edge.

Rectangular Prism (Cuboid)

Volume: $V = l \times w \times h$

Surface Area: $SA = 2(lw + lh + wh)$

Where $l$ is length, $w$ is width, and $h$ is height.

Sphere

Volume: $V = \frac{4}{3} \pi r^3$

Surface Area: $SA = 4 \pi r^2$

Where $r$ is the radius.

Cylinder

Volume: $V = \pi r^2 h$

Surface Area: $SA = 2 \pi r (r + h)$

Where $r$ is the radius of the base and $h$ is the height.

Cone

Volume: $V = \frac{1}{3} \pi r^2 h$

Surface Area: $SA = \pi r (r + l)$

Where $r$ is the radius, $h$ is the vertical height, and $l$ is the slant height.

Note: To find slant height ($l$), use $l = \sqrt{r^2 + h^2}$.

Pyramid

Volume: $V = \frac{1}{3} \times b \times h$

Surface Area: $SA = b + \frac{1}{2} \times p \times l$

Where $b$ is the area of the base, $h$ is the height, $p$ is the perimeter of the base, and $l$ is the slant height.

Coordinate Geometry Formulas

Coordinate geometry (or analytic geometry) defines geometric positions using numbers on a coordinate plane. These are useful for finding distances and midpoint positions between points.

Distance Formula

$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Where $(x_1, y_1)$ and $(x_2, y_2)$ are two points on the coordinate plane.

Midpoint Formula

$M = \left(\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2}\right)$

Where $(x_1, y_1)$ and $(x_2, y_2)$ are the endpoints of the line segment.

Slope Formula

$m = \frac{y_2 - y_1}{x_2 - x_1}$

Where $m$ is the slope of the line passing through $(x_1, y_1)$ and $(x_2, y_2)$.

Equation of a Line (Slope-Intercept Form)

$y = mx + b$

Where $m$ is the slope and $b$ is the y-intercept.

Conclusion

Mastering these geometry formulas provides a strong foundation for advancing in mathematics, science, engineering, and art. While memorization is helpful, understanding the derivation and application of these formulas ensures better problem-solving skills. Keep this list handy as a reference for your geometry studies or professional projects.

Reference Files For Geometry Formulas List

Screenshoot