This document contains formulas for calculating properties of common geometric shapes such as triangles, rectangles, circles, spheres, and coordinate geometry. It includes formulas for: - Calculating the perimeter, area, and properties of triangles like the Pythagorean theorem - Calculating the perimeter, area, and properties of quadrilaterals like squares, rectangles, parallelograms, and trapezoids - Calculating circumference, arc length, sectors, and properties of circles - Calculating surface area and volume of three-dimensional shapes like cubes, cylinders, cones, and spheres - Calculating distance, midpoints, slopes and the general form of lines in coordinate geometry

1. Geometry Formulas
Triangle Formula
Pythagorean Theorem ܽଶ
൅ ܾଶ
ൌ ܿଶ
45º-45º-90º Phenomenon
‫:ݔ‬ ‫:ݔ‬ ‫2√ݔ‬
h=‫2√ݔ‬
30º-60º-90º Phenomenon
ܾ ൌ ‫3√ݔ‬
‫:ݔ‬ ‫:3√ݔ‬ 2‫ݔ‬
Perimeter s1+s2+s3
Area of any Triangle
1
2
ሺ‫ܪܤ‬ሻ
Area of Isosceles Triangle
1
2
ሺ݈݁݃ሻଶ
Area of Right Triangle
1
2
ሺ‫ܮ‬ଵ ൉ ‫ܮ‬ଶሻ
Area of Equilateral Triangle
‫ݏ‬ଶ
√3
4
Square Formula
Perimeter 4S
Area #1 S2
Area #2 1
2ൗ ‫݈ܽ݊݋݃ܽ݅ܦ‬ଶ
Relationship between Side & Diagonal
ܵ ൌ
‫ܦ‬
√2
D = S2
Rectangle Formula
Perimeter 2ሺ‫ܮ‬ ൅ ܹሻ
Area #1 ‫ܮ‬ ൉ ܹ
Relationship between Side & Diagonal ‫݄ݐ݃݊݁ܮ‬ଶ
൅ ܹ݅݀‫݄ݐ‬ଶ
ൌ ‫݈ܽ݊݋݃ܽ݅ܦ‬ଶ
Parallelogram Formula
Perimeter 2ሺ‫ܮ‬ ൅ ܹሻ
Area ‫ܤ‬ ൉ ‫ܪ‬
Rhombus Formula
Perimeter 4ܵ
Area #1 ‫ܤ‬ ൉ ‫ܪ‬
Area #2
1
2
ሺ݀ଵ ൉ ݀ଶሻ

2. Trapezoid Formula
Perimeter ‫ܤ‬ଵ ൅ ‫ܤ‬ଶ ൅ ܵଵ ൅ ܵଶ
Area
1
2
ሺ‫݁ݏܽܤ‬ଵ ൅ ‫݁ݏܽܤ‬ଶሻ ൉ ‫ݐ݄݃݅݁ܪ‬
Circumference Formula
Circumference #1 ߨ݀
Circumference #2 2ߨ‫ݎ‬
Diameter
‫ܥ‬
ߨ
Radius
‫ܥ‬
2ߨ
Arc of Circle Formula
Arc Length (Central)
‫ݏ݁݁ݎ݃݁ܦ‬ ‫݂݋‬ ‫݈ܽݎݐ݊݁ܥ‬ ‫݈݁݃݊ܣ‬
360º
൉ ‫ܥ‬
Arc Length (Inscribed)
2 ൉ ‫ݏ݁݁ݎ݃݁ܦ‬ ‫݂݋‬ ‫ܾ݀݁݅ݎܿݏ݊ܫ‬ ‫݈݁݃݊ܣ‬
360º
൉ ‫ܥ‬
Arc of Circle Formula
Arc Measure (Intersecting Chords) [1] ൏ ܲ ൌ൏ ܳ ൌ
‫ܥܣ‬෢ ൅ ‫ܦܤ‬෢
2
Arc Measure (Intersecting
Secants/Tangents) [2] ൏ ‫ܥ‬ ൌ
‫ܦܣ‬෢ ൅ ‫ܦܤ‬෢
2
Perimeter of Sector of Circle Arc Measure + 2r
A
C
D
B
P Q
A
B
C
D
1 2

3. Circle Formula
Area of Circle #1 ߨ‫ݎ‬ଶ
Area of Circle #2 ߨ
݀ଶ
4
Sector of Circle Formula
Area of Sector
‫ݏ݁݁ݎ݃݁ܦ‬ ‫݂݋‬ ‫݈ܽݎݐ݊݁ܥ‬ ‫݈݁݃݊ܣ‬
360º
൉ ‫ܽ݁ݎܣ‬ ‫݈݁ܿݎ݅ܥ‬
Rectangular Solids Formula
Area of Front & Back Faces 2ሺ‫݄ݐ݃݊݁ܮ‬ ൉ ‫ݐ݄݃݅݁ܪ‬ሻ
Area of Top & Bottom Faces 2ሺ‫݄ݐ݃݊݁ܮ‬ ൉ ܹ݅݀‫݄ݐ‬ሻ
Area of Front & Back Faces 2ሺܹ݅݀‫݄ݐ‬ ൉ ‫ݐ݄݃݅݁ܪ‬ሻ
Total Surface 2ሺ‫ܪܮ‬ ൅ ‫ܹܮ‬ ൅ ܹ‫ܪ‬ሻ
Diagonal ‫ܦ‬ ൌ ඥ‫ܮ‬ଶ ൅ ܹଶ ൅ ‫ܪ‬ଶ
Cube Formula
Area of Cube 6ܵଶ
Volume ܵଷ
Diagonal
‫ܦ‬ ൌ ܵ√3
ܵ ൌ
‫ܦ‬
√3
Cylinder Formula
Area of Top & Bottom Circular Bases ߨ‫ݎ‬ଶ
൅ ߨ‫ݎ‬ଶ
ൌ 2ߨ‫ݎ‬ଶ
Lateral Surface Area 2ߨ‫݄ݎ‬
Total Surface Area 2ߨ‫ݎ‬ଶ
൅ 2ߨ‫݄ݎ‬
Volume ߨ‫ݎ‬ଶ
݄

4. Cone Formula
Surface Area ߨ‫݈ݎ‬ ൅ ߨ‫ݎ‬ଶ
Volume of Cone 1
3
ߨ‫ݎ‬ଶ
݄
1/3 (area of Cylinder)
Sphere Formula
Surface Area 4ߨ‫ݎ‬ଶ
Volume
4
3
ߨ‫ݎ‬ଷ
Coordinate geometry Formula
Distance ඥሺ‫ݔ‬ଵ െ ‫ݔ‬ଶሻଶ ൅ ሺ‫ݕ‬ଵ െ ‫ݕ‬ଶሻଶ
Mid-point ሺ
‫ݔ‬ଵ ൅ ‫ݔ‬ଶ
2
,
‫ݕ‬ଵ ൅ ‫ݕ‬ଶ
2
ሻ
General Form ‫ݕ‬ ൌ ݉‫ݔ‬ ൅ ܾ
Slope
‫ݕ‬ଵ െ ‫ݕ‬ଶ
‫ݔ‬ଵ െ ‫ݔ‬ଶ