Geometric Shapes - Areas
Square
The area of a square can be calculated as
A = a2 (1a)
The side of a square can be calculated as
a = A1/2 (1b)
The diagonal of a square can be calculated as
d = a 21/2 (1c)
Rectangle
The area of a rectangle can be calculated as
A = a b (2a)
The diagonal of a rectangle can be calculated as
d = (a2 + b2)1/2 (2b)
Parallelogram
The area of a parallelogram can be calculated as
A = a h
= a b sin(α) (3a)
The diameters of a parallelogram can be calculated as
d1 = ((a + h cot(α))2 + h2)1/2 (3b)
d2 = ((a - h cot(α))2 + h2)1/2 (3b)
Equilateral Triangle
An equilateral triangle is a triangle in which all three sides are equal.
The area of an equilateral triangle can be calculated as
A = a2 / 3 31/2 (4a)
The area of an equilateral triangle can be calculated as
h = a / 2 31/2 (4b)
Triangle
The area of a triangle can be calculated as
A = a h / 2
= r s (5a)
r = a h / 2s (5b)
R = b c / 2 h (5c)
s = (a + b + c) / 2 (5d)
x = s - a (5e)
y = s - b (5f)
z = s - c (5g)
Trapezoid
The area of a trapezoid can be calculated as
A = 1/2 (a + b) h
= m h (6a)
m = (a + b) / 2 (6b)
Hexagon
The area of a hexagon can be calculated as
A = 3/2 a2 31/2 (7a)
d = 2 a
= 2 / 31/2 s
= 1.1547005 s (7b)
s = 31/2/ 2 d
= 0.866025 d (7c)
Circle
The area of a circle can be calculated as
A = π/4 d2
= π r2
= 0.785.. d2 (8a)
C = 2 π r
= π d (8b)
where
C = circumference
Sector and Segment of a Circle
Sector of Circle
Area of a sector of circle can be expressed as
A = 1/2 θr r2 (9)
= 1/360 θd π r2
where
θr = angle in radians
θd = angle in degrees
Segment of Circle
Area of a segment of circle can be expressed as
A = 1/2 (θr - sin(θr)) r2
= 1/2 (π θd / 180 - sin(θd)) r2 (10)
Right Circular Cylinder
Lateral surface area of a right circular circle can be expressed as
A = 2 π r h (11)
where
h= height of cylinder (m, ft)
r = radius of base (m, ft)
Right Circular Cone
Lateral surface area of a right circular cone can be expressed as
A = π r l
= π r (r2 + h2)1/2 (12)
where
h= height of cone (m, ft)
r = radius of base (m, ft)
l = slant length (m, ft)
Sphere
Lateral surface area of a sphere can be expressed as
A = 4 π r2 (13)
Related Topics
• Mathematics
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Related Documents
Area of Intersecting Circles
Calculate area of intersecting circles
Area Units Converter
Convert between units of area.
Centroids of Plane Areas
The controid of square, rectangle, circle, semi-circle and right-angled triangle.
Circle - the Chord Lengths when Divided in to Equal Segments
Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
Circle Equation
The equation for a circle
Circles - Circumferences and Areas
Circumferences and areas of circles with diameters in inches.
Circles on the Outside of a Circle
Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.
Cylindrical Tanks - Volumes
Volume in US gallons and liters.
Elementary Curves
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.
Equal Areas - Circles vs. Squares
Radius and side lengths of equal areas, circles and squares.
Exponents - Powers and Roots
The laws of fractional and integer exponents.
Factorials
The product of all positive integers.
Hexagons and Squares - Diagonal Lengths
Distances between corners for hexagons and squares.
Length of a Spiral
Calculate the length of a spiral or the length of material contained in a roll.
Maximizing Space: Fit Small Rectangles Inside a Larger Rectangle
The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).
Oblique Triangle
Calculate oblique triangles.
Pythagorean Theorem
Verifying square corners.
Right Angled Triangle
Right angled triangle equations.
Squaring with Diagonal Measurements
A rectangle is square if the lengths of both diagonals are equal.
Trigonometric Functions
Sine, cosine and tangent - the natural trigonometric functions.