geometry formulas cheat sheet

3 min read 22-10-2024

Geometry Formulas Cheat Sheet: A Quick Reference Guide

Geometry, the study of shapes and their properties, is a fundamental part of mathematics. Whether you're a student tackling homework or an adult looking to refresh your knowledge, having a quick reference guide for essential geometry formulas can be incredibly helpful.

This cheat sheet will cover some of the most common geometric formulas, organized by shape. We'll also provide examples and explanations to make the concepts easier to grasp.

Let's dive in!

1. Triangles

1.1 Area

Formula: Area = (1/2) * base * height
Explanation: The area of a triangle is half the product of its base and height.
Example: A triangle with a base of 6 cm and a height of 4 cm has an area of (1/2) * 6 cm * 4 cm = 12 cm².

1.2 Perimeter

Formula: Perimeter = sum of all sides
Explanation: The perimeter of a triangle is the total length of its sides added together.
Example: A triangle with sides of 3 cm, 4 cm, and 5 cm has a perimeter of 3 cm + 4 cm + 5 cm = 12 cm.

1.3 Pythagorean Theorem

Formula: a² + b² = c²
Explanation: This theorem applies to right-angled triangles, where 'c' represents the hypotenuse (the side opposite the right angle) and 'a' and 'b' represent the other two sides.
Example: If a right triangle has sides of 3 cm and 4 cm, the hypotenuse 'c' can be found by: 3² + 4² = c²; 9 + 16 = c²; c² = 25; c = 5 cm.

1.4 Types of Triangles

Equilateral: All sides are equal, and all angles are 60 degrees.
Isosceles: Two sides are equal, and the angles opposite those sides are equal.
Scalene: All sides are different lengths, and all angles are different.
Right-angled: One angle is 90 degrees.

2. Squares

2.1 Area

Formula: Area = side²
Explanation: The area of a square is the product of its side length multiplied by itself.
Example: A square with a side of 5 cm has an area of 5 cm * 5 cm = 25 cm².

2.2 Perimeter

Formula: Perimeter = 4 * side
Explanation: The perimeter of a square is the sum of the lengths of all its sides.
Example: A square with a side of 5 cm has a perimeter of 4 * 5 cm = 20 cm.

3. Rectangles

3.1 Area

Formula: Area = length * width
Explanation: The area of a rectangle is the product of its length and width.
Example: A rectangle with a length of 8 cm and a width of 3 cm has an area of 8 cm * 3 cm = 24 cm².

3.2 Perimeter

Formula: Perimeter = 2 * (length + width)
Explanation: The perimeter of a rectangle is twice the sum of its length and width.
Example: A rectangle with a length of 8 cm and a width of 3 cm has a perimeter of 2 * (8 cm + 3 cm) = 22 cm.

4. Circles

4.1 Area

Formula: Area = π * radius² (where π ≈ 3.14159)
Explanation: The area of a circle is the product of pi (π) and the square of its radius.
Example: A circle with a radius of 4 cm has an area of 3.14159 * 4 cm * 4 cm = 50.26548 cm².

4.2 Circumference

Formula: Circumference = 2 * π * radius = π * diameter
Explanation: The circumference of a circle is the distance around its outer edge. It can be calculated using the radius or the diameter.
Example: A circle with a radius of 4 cm has a circumference of 2 * 3.14159 * 4 cm = 25.13274 cm.

5. Cubes

5.1 Volume

Formula: Volume = side³
Explanation: The volume of a cube is the product of its side length multiplied by itself three times.
Example: A cube with a side of 3 cm has a volume of 3 cm * 3 cm * 3 cm = 27 cm³.

5.2 Surface Area

Formula: Surface Area = 6 * side²
Explanation: The surface area of a cube is the sum of the areas of all its faces.
Example: A cube with a side of 3 cm has a surface area of 6 * 3 cm * 3 cm = 54 cm².

6. Rectangular Prisms

6.1 Volume

Formula: Volume = length * width * height
Explanation: The volume of a rectangular prism is the product of its length, width, and height.
Example: A rectangular prism with a length of 5 cm, a width of 4 cm, and a height of 3 cm has a volume of 5 cm * 4 cm * 3 cm = 60 cm³.

6.2 Surface Area

Formula: Surface Area = 2 * (length * width + length * height + width * height)
Explanation: The surface area of a rectangular prism is the sum of the areas of all its faces.
Example: A rectangular prism with a length of 5 cm, a width of 4 cm, and a height of 3 cm has a surface area of 2 * (5 cm * 4 cm + 5 cm * 3 cm + 4 cm * 3 cm) = 94 cm².

Remember:

These formulas are just a starting point. Many other geometric shapes and formulas exist.
Always label your units of measurement (cm, m, etc.) to ensure accurate calculations.
Familiarize yourself with the different types of geometric shapes and their unique properties.

Using this cheat sheet, you'll be well on your way to confidently tackling any geometric problem!

geometry formulas cheat sheet