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Geometric Shapes

Annulus

annulus shape
Annulus Calculator

Annulus Formulas
  • Outer Circumference = C1 = 2πr1
  • Inner Circumference = C2 = 2πr2
  • Surface Area of Large Circle = A1 = πr12
  • Surface Area of Small Circle = A2 = πr22
  • Surface Area of Annulus (gray shaded area) = A0 = A1 - A2
    = (πr12) - (πr22)
    = π(r12 - r22)

Circle

circle shape
Circle Calculator

Circle Formulas
  • Diameter = 2π
  • Circumference = 2πr
  • Area = πr2

Circular Sector

circular sector shape


Circular Sector Formulas
  • Arc Length = s = rΘ
  • Chord = c = 2r sin(1/2Θ)
  • Area of Minor Sector = 1/2rs
  • Area of Major Sector = πr2 - 1/2rs

Circular Segment

circular segment shape


Circular Segment Formulas
  • Arc Length = s = rΘ
  • Chord = c = 2r sin(1/2Θ)
  • Area of Segment = AreaSector - AreaIsoceles Triangle
    = 1/2rs - 1/2cm

Parallelogram

parallelogram shape
Parallelogram Calculator

Parallelogram Formulas
  • Perimeter = 2a + 2b
  • Area = bh = ab sin(A) = ab sin(B), with A and B in radians
  • Height = h = a sin(A) = a sin(B), with A and B in radians
  • Angles
    • A = C
    • B = D
    • A + B = 180° = π radians
  • Diagonals
    • p = √(a2 + b2 - 2ab cos(A)) = √(a2 + b2 + 2ab cos(B))
    • q = √(a2 + b2 + 2ab cos(A)) = √(a2 + b2 - 2ab cos(B))
    • p2 + q2 = 2(a2 + b2)

Polygons

polygon shape
Polygon Calculator

Polygon Formulas
  • Side Length a
    • a = 2r tan(π/n) = 2R sin(π/n)
  • Inradius r
    • r = (1/2)a cot(π/n) = R cos(π/n)
  • Circumradius R
    • R = (1/2) a csc(π/n) = r sec(π/n)
  • Area A
    • A = (1/4)na2 cot(π/n) = nr2 tan(π/n)
  • Perimeter P
    • P = na
  • Interior Angle x
    • x = ((n-2)π / n) radians = (((n-2)/n) x 180° ) degrees
  • Exterior Angle y
    • y = (2π / n) radians = (360° / n) degrees
    • polygon interior and exterior angles

Rectangle

rectangle shape
Rectangle Calculator

Rectangle Formulas
  • Perimeter = 2a + 2b
  • Area = ab
  • Diagonals = p = q = √(a2 + b2)

Rhombus

rhombus shape labeled with angles, sides and diagonals
rhombus shape labeled with angles, side and height
Rhombus Calculator

Rhombus Formulas ***need to check formulas for diagonals***
  • Perimeter = 4a
  • Area = ah = a2 sin(A) = a2 sin(B) = pq/2, with A and B in radians
  • Height = h = a sin(A) = a sin(B), with A and B in radians
  • Angles
    • A = C
    • B = D
    • A + B = 180° = π radians
  • Diagonals
    • p = a√(2 - 2 cos(A)) = a√(2 + 2 cos(B))
    • q = a√(2 + 2 cos(A)) = a√(2 - 2 cos(B))
    • p2 + q2 = 4a2

Square

square shape
Square Calculator

Square Formulas
  • Perimeter = 4a
  • Area = a2
  • Diagonal = √(2a2) = a√2

Stadium

stadium shape
Stadium Calculator

Stadium Formulas
  • Perimeter = 2(πr + a)
  • Area = πr2 + 2ra
  • Dotted Line = diameter of the circle = 2r

Triangle: Equilateral

equilateral triangel shape
Triangle Calculator: Equilateral

Triangle Formulas
  • Perimeter = a + b + c
  • Area = 1/2bh = bh/2

Triangle: Isosceles

isosceles triangle shape


Triangle Formulas
  • Perimeter = a + b + c
  • Area = 1/2bh = bh/2

Triangle: Right

right triangle shape
Triangle Calculator: Right

Triangle Formulas
  • Perimeter = a + b + c
  • Area = 1/2bh = bh/2


 

Cite this content, page or calculator as:

Furey, Edward "Geometric Shapes in Plane Geometry"; from https://www.calculatorsoup.com - Online Calculator Resource.

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