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