Helpful Geometry Formulas

Geometry Formulas

Triangle

Formula

Pythagorean Theorem

ܽଶ ൅ ܾ ଶ ൌ ܿ ଶ

45º-45º-90º Phenomenon

30º-60º-90º Phenomenon

h=‫2√ݔ‬

‫2√ݔ :ݔ :ݔ‬

ܾ ൌ ‫3√ݔ‬

‫ݔ2 :3√ݔ :ݔ‬

Perimeter

s1+s2+s3

Area of any Triangle

1

ሺ‫ܪܤ‬ሻ

2

Area of Isosceles Triangle

1

ሺ݈݁݃ሻଶ

2

Area of Right Triangle

1

ሺ‫ ܮ‬൉ ‫ ܮ‬ሻ

2 ଵ ଶ

Area of Equilateral Triangle

‫ ݏ‬ଶ √3

4

Square

Formula

Perimeter

4S

Area #1

S2

Area #2

1ൗ ‫ ݈ܽ݊݋݃ܽ݅ܦ‬ଶ

2

D = S2

Relationship between Side & Diagonal

ܵൌ

‫ܦ‬

√2

Rectangle

Formula

Perimeter

2ሺ‫ ܮ‬൅ ܹሻ

Area #1

‫ܮ‬൉ܹ

Relationship between Side & Diagonal

‫݄ݐ݃݊݁ܮ‬ଶ ൅ ܹ݅݀‫݄ݐ‬ଶ ൌ ‫ ݈ܽ݊݋݃ܽ݅ܦ‬ଶ

Parallelogram

Formula

Perimeter

2ሺ‫ ܮ‬൅ ܹሻ

Area

‫ܤ‬൉‫ܪ‬

Rhombus

Formula

Perimeter

4ܵ

Area #1

‫ܤ‬൉‫ܪ‬

1

ሺ݀ ൉ ݀ ሻ

2 ଵ ଶ

Area #2

Trapezoid

Formula

Perimeter

‫ܤ‬ଵ ൅ ‫ܤ‬ଶ ൅ ܵଵ ൅ ܵଶ

1

ሺ‫݁ݏܽܤ‬ଵ ൅ ‫݁ݏܽܤ‬ଶ ሻ ൉ ‫ݐ݄݃݅݁ܪ‬

2

Area

Circumference

Formula

Circumference #1

ߨ݀

Circumference #2

2ߨ‫ݎ‬

‫ܥ‬

ߨ

‫ܥ‬

2ߨ

Diameter

Radius

Arc of Circle

Formula

‫݈݁݃݊ܣ ݈ܽݎݐ݊݁ܥ ݂݋ ݏ݁݁ݎ݃݁ܦ‬

൉‫ܥ‬

360º

2 ൉ ‫݈݁݃݊ܣ ܾ݀݁݅ݎܿݏ݊ܫ ݂݋ ݏ݁݁ݎ݃݁ܦ‬

൉‫ܥ‬

360º

Arc Length (Central)

Arc Length (Inscribed)

A

D

D

P

C

Q

B

C

B

A

2

1

Arc of Circle

Formula

Arc Measure (Intersecting Chords) [1]

൏ ܲ ൌ൏ ܳ ൌ

Arc Measure (Intersecting

Secants/Tangents) [2]

൏‫ܥ‬ൌ

Perimeter of Sector of Circle

Arc Measure + 2r

෢

෢

‫ ܥܣ‬൅ ‫ܦܤ‬

2

෢

෢

‫ ܦܣ‬൅ ‫ܦܤ‬

2

Circle

Formula

Area of Circle #1

ߨ‫ ݎ‬ଶ

Area of Circle #2

ߨ

Sector of Circle

Formula

Area of Sector

‫݈݁݃݊ܣ ݈ܽݎݐ݊݁ܥ ݂݋ ݏ݁݁ݎ݃݁ܦ‬

൉ ‫݈݁ܿݎ݅ܥ ܽ݁ݎܣ‬

360º

Rectangular Solids

Formula

Area of Front & Back Faces

2ሺ‫ ݄ݐ݃݊݁ܮ‬൉ ‫ݐ݄݃݅݁ܪ‬ሻ

Area of Top & Bottom Faces

2ሺ‫ ݄ݐ݃݊݁ܮ‬൉ ܹ݅݀‫݄ݐ‬ሻ

Area of Front & Back Faces

2ሺܹ݅݀‫ ݄ݐ‬൉ ‫ݐ݄݃݅݁ܪ‬ሻ

Total Surface

2ሺ‫ ܪܮ‬൅ ‫ ܹܮ‬൅ ܹ‫ܪ‬ሻ

Diagonal

‫ ܦ‬ൌ ඥ‫ܮ‬ଶ ൅...