Geometry formulas

Plane Geometry

Triangle The perimeter = the sum of all sides, i.e.: P=AB+BC+CA Surface = (height x base)/2, i.e.: Striangle = (b x h)/2. In our case, b=BC, and h=AD. So though, SABC=(BCxAD)/2

Parallelogram The perimeter = the sum of all sides, i.e.: P=AB + BC + CD + DA. Since opposite sides of the parallelogram are congruent (equal), the perimeter can be calculated as P=2(AB + BC). Parallelogram's Surface = base x height, i.e. Sparallelogram=b x h, and on our case, SABCD=DC x AM, because DC = b (base) and AM = h (height).

Rectangle The rectangle has length( L=AB) and width(l=BC). The perimeter = the sum of all sides, i.e.: P=AB+BC+CD+DA or P=2(L+l) Rectangle's Surface = length x width Srectangle = L x l. In our particular case SABCD=AB x BC.

Square The square is a rectangle that has all sides equal (congruent), equal to the width or length. The perimeter = the sum of all sides, i.e.: P=AB+BC+CD+DA or P=4 L, where L is sides of the square (AB=BC=CD=DA=L). Square's Surface =  L2. In our case, SABCD=AB2.

Trapezium The perimeter = the sum of all sides, i.e.: P=AB + BC + CD + DA. Trapezium Area = (Big Base + Small Base) x Height / 2, i.e Atrapezium=(B + b) x h/2, and for our figure we have AABCD = (DC + AB) x AM/2, because DC = B (Big Base) AB = b  (Small Base), and AM = h (Height).

The Circle We have OA - the Radius (not. r) The Circle's Length (the circumference of the circle): The Circle's Area (Surface): Solid Geometry

The Pyramid We discuss about regular solids, and so is regular pyramid. We have: AB - the base edge(not. m) VA - the laterla edge(not. l) VO - the height of the Pyramid (not. h) VM - apotema side or pyramid apotema (not. ap) OM - apotema base (not. ab). The Lateral Area (of the Pyramid) = sum of the areas of the side faces      Alat = (Pb x ap) / 2. The Base Area      Ab = (Pb x ab) / 2, where Pb is base's perimeter The Total Area = Base Area + Lateral Area The Volume      Vpir=(Ab x h) / 3. Tetrahedron can be considered a pyramid whose base a triangle, area and volume are computed analog.

Cuboid, parallelepiped, prism We have: AB - length(not. L) BC - width(not. l) AE - height or lateral edge (not. h)      Lateral Surface (Area) = The sum of all lateral sides      Alat = Pb x h, where Pb is the base perimeter, or      Alat = 2(L + l) x h The Base Area      Ab = L x l. Total Area (Surface) = Base Area + Lateral Area The Volume      Vcuboid = Ab x h or     Vcuboid = L x l x h. Cuboid is a particular case of light and the cube is a cuboid particular case, in that it is a cuboid with all sides congruent. Therefore we do not remember anything about them here.

The Truncated Pyramid We have: AB - The Edge of Big Base A'B' - The Edge of Small (Top) Base OO' - Height (not. h) AA' - The Lateral Edge OM - The Apotema of Big Base (not. aB) O'M' - The Apotema of Small Base (not. ab) MM' - The Apotema of the Truncated Pyramid (not. at)      The Lateral Area (Surface) = The sum of all lateral sides Areas      Alat = (PB + Pb) at / 2, where Pb is the perimeter of small base, and PB is the perimeter of big base.      Ab=Pb x ab.      AB=PB x aB. Total Area = Big Base Area + Small Base Area + Lateral Area The Volume      Vtruncated pyramid = The cilinder We have: AA' - generator edge (not. g) OO' - the height of the cilinder (not. h; at our particular case, at right circular cylinder, we have g=h) AO - base radius (not. r) Base Area = the area of the base circle, i.e.: Lateral Area: Total Area: The Volume of the Cilinder: The Cone We have: VA - the generator (not. g) VO - Cone's Height (not. h) AO - Base's radius (not. r) Base Area = The surface of base circle, i.e.: Lateral Area: Total Area: The Volume: Frustoconic We have: A'A - generator (not. G) OO' - frustoconic's Height (not. I) AO - Big Base Radius (not. R) A'O' - Small Base Radius(not. r) Lateral Area: Total Area: The Volume: The Sphere We have: OA - Radius (not. r) Area of the Sphere: The Volume: _________________________________

Keywords: formulas geometry, geometric body volume formula, trapezoid, square, rectangle, triangle, sphere

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