Plane and Solid Geometry

Description Formula(s) Definitions

Sum of interior angles of regular polygons

Size of each interior angle

Number of diagonals in a polygon

Sum of exterior angles in a polygon

Size of each exterior angle

Area of a regular polygon given apothem and perimeter

Area and perimeter of regular polygon given number of sides and

apothem

Area and perimeter of regular polygon given number of sides and

length of one side

Area and perimeter of regular polygon inscribed in a circle

Area of a pentagram

Area of a hexagram

Area and perimeter of a square

Area and perimeter of a rectangle

Area of a parallelogram

Area of a trapezoid

Area of a rhombus

Semiperimeter

Area of a general quadrilateral

Area of a polygon with inscribed circle

Ptolemy’s theorem for a cyclic quadrilateral

Bramaguptha’s Formula for a Cyclic Quadrilateral (A, r)

Area of a quadrilateral circumscribing a circle

Secant-secant theorem

Secant-tangent theorem

Cross-chord theorem

Tangent-tangent theorem

Circumference and area of circle

Circular sector (A and S)

Circular segment

Cubic area and volume

Rectangular parallepiped area and volume

Prism volume (2) and lateral area

Circular cylinder lateral area and volume (2)

Right circular cylinder lateral area and volume

Volume of truncated prism

Cone lateral area and volume

Cone frustum lateral area and volume

Pyramid lateral area and volume

Pyramidal frustum lateral area and volume

Volume of prismatoid

Volume and area of a sphere

Area of a spherical zone

Area and volume of a spherical segment given radius and height

Area and volume of a spherical segment given upper and lower

bases and height

Volume of a spherical sector

Spherical excess

Area of a spherical polygon

Volume and area of spherical pyramid

Area of spherical lune

Area of spherical wedge