Posts for Tag: Geometry

Regular Tetrahedron Formulas

A regular tetrahedron is a tetrahedron in which all four faces are equilateral triangles. It is one of the five regular Platonic solids, which have been known since antiquity. Triangle side length: a Height: h Area of base: SB Total Surface Area: S Volume: V $h=√{2/3}\ a $ $S_B=√3/4\ a^2$ $S=√3\ a^2 $ $V=1/3S_B\ h=a^3/{6√2}$

Prism Formulas

In geometry, a prism is a polyhedron comprising an n-sided polygonal base, a second base which is a translated copy (rigidly moved without rotation) of the first, and n other faces (necessarily all parallelograms) joining corresponding sides of the two bases. All cross-sections parallel to the bases are translations of the bases. Lateral edge: lRead More

Rectangular Parallelepiped Formulas

A three-dimensional figure all of whose face angles are right angles, so all its faces are rectangles and all its dihedral angles are right angles. Edges: a,b,c Diagonal: d Surface area: S Volume: V $d=√{a^2+b^2+c^2}$ $S=2(ab+ac+bc)$ $V=abc$

Cube Formulas

In geometry, a cube is a three-dimensional solid object bounded by six square faces, facets or sides, with three meeting at each vertex. Edge: a Space diagonal: d Face diagonal: df Radius of inscribed sphere: r Radius of circumscribed sphere: R Surface area: S Volume: V $d=a√3$ $d_f=a√2$ $r=a/2$ $R=√3/2a$ $S=6a^2$ $V=a^3$ angles between faces:Read More

Circle Segment Formulas

In geometry, a circular segment (symbol: ⌓) is a region of a circle which is “cut off” from the rest of the circle by a secant or a chord. Radius of circle: R Arc length: s Chord: a Central angle (in radians): x Central angle (in degrees): α Height of the segment: h Perimeter: LRead More

Circle Sector Formulas

A circular sector or circle sector (symbol: ⌔), is the portion of a circle enclosed by two radii and an arc, where the smaller area is known as the minor sector and the larger is known as the major sector. Radius: R Arc length: s Central angle (in radians): x Central angle (in degrees): αRead More

Circle Formulas, Algebra

A circle is a simple closed shape. It is the set of all points in a plane that are at a given distance from a given point, the centre; equivalently it is the curve traced out by a point that moves so that its distance from a given point is constant. Radius: R Diameter: dRead More

Regular Polygon Formulas

In Euclidean geometry, a regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length). Regular polygons may be either convex or star. We will discuss the property of regular convex polygon here. Side length: a Number of sides: n Internal angle: α SlantRead More

Regular Hexagon Formulas

In Euclidean plane geometry, a Regular Hexagon is a Hexagon having all sides are the same length (congruent) and all interior angles are the same size (congruent). Side: a Internal angle: α Slant height: m Radius of circumscribed circle: R Radius of inscribed circle: r Perimeter: L Semiperimeter: p Area: S $α=120°$ $r=m={a√3}/2$ $R=a$ $L=6a$Read More

General Quadrilateral Formula

In Euclidean plane geometry, a quadrilateral is a polygon with four edges (or sides) and four vertices or corners. Sides of quadrilateral: a,b,c,d Diagonals: d1,d2 Angle between the diagonals: φ Internal angles: α,β,γ,δ Perimeter: L Area: S $α+β+γ+δ=360°$ $L=a+b+c+d$ $S=1/2d_1d_2\ sin\ φ$