Geometry Formulas Cheat Sheet

This geometry formulas cheat sheet gives the main formulas for area, perimeter, circumference, surface area, and volume in one place. Use it to match the right formula to the right shape before you start calculating.

Geometry Formulas for 2D and 3D Shapes

2D Shapes

Shape	What you want	Formula
Square	Perimeter	$P = 4s$
Square	Area	$A = s^2$
Rectangle	Perimeter	$P = 2l + 2w$
Rectangle	Area	$A = lw$
Triangle	Perimeter	$P = a + b + c$
Triangle	Area	$A = \frac\{1\}\{2\}bh$
Parallelogram	Area	$A = bh$
Trapezoid	Area	$A = \frac\{1\}\{2\}(b_1 + b_2)h$
Circle	Circumference	$C = 2\pi r$
Circle	Area	$A = \pi r^2$

3D Solids

Solid	What you want	Formula
Rectangular prism	Volume	$V = lwh$
Rectangular prism	Surface area	$SA = 2lw + 2lh + 2wh$
Cylinder	Volume	$V = \pi r^2 h$
Cylinder	Surface area	$SA = 2\pi rh + 2\pi r^2$
Cone	Volume	$V = \frac\{1\}\{3\}\pi r^2 h$
Cone	Surface area	$SA = \pi r\ell + \pi r^2$
Sphere	Volume	$V = \frac\{4\}\{3\}\pi r^3$
Sphere	Surface area	$SA = 4\pi r^2$

For the cone surface area formula, $\ell$ is the slant height, not the vertical height. That condition matters.

How To Pick the Right Geometry Formula

Start with the shape. A circle formula will not help with a triangle, and a 2D area formula will not answer a 3D volume question.

Then ask what kind of measurement the problem wants:

1. Use perimeter or circumference for distance around a shape.
2. Use area for the flat space inside a 2D shape.
3. Use surface area for the total outside covering of a 3D solid.
4. Use volume for the space inside a 3D solid.

That quick check prevents many wrong answers.

Worked Example: Triangle Area

Find the area of a triangle with base $10$ cm and perpendicular height $6$ cm.

Use the triangle area formula:

$$A = \frac{1}{2}bh$$

Substitute the measurements:

$$A = \frac{1}{2}(10)(6) = 30$$

So the area is $30$ square centimeters, or $30\ \mathrm{cm}^2$.

This example is useful because it shows the role of the perpendicular height. If the given $6$ cm were just a slanted side and not perpendicular to the base, the formula would not apply as written.

Common Geometry Formula Mistakes

1. Mixing up area and perimeter. Area uses square units, while perimeter uses linear units.
2. Using diameter when the formula expects radius. If $d$ is given for a circle, convert with $r = \frac{d}{2}$ first.
3. Using the wrong height. In formulas like $A = \frac{1}{2}bh$, the height must be perpendicular to the base.
4. Forgetting units. A rectangle with side lengths in meters has area in square meters, not meters.
5. Applying a memorized formula to the wrong shape just because the variables look familiar.

When Geometry Formulas Are Used

Geometry formulas show up in school math, construction, design, engineering, and everyday estimation. You might use them to find flooring area, fencing length, container volume, or the amount of material needed to cover a surface.

Even when software does the arithmetic, knowing which formula fits the shape helps you catch bad inputs and unreasonable results.

Try a Similar Problem

Try finding the circumference and area of a circle with radius $4$ units. Using the same radius in both formulas is a good way to see the difference between a linear measure, $C = 2\pi r$, and a square measure, $A = \pi r^2$.