= 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)
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)
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)
The area of a trapezoid can be calculated as
A = 1/2 (a + b) h
= m h (6a)
m = (a + b) / 2 (6b)
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)
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
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
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)
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)
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)
Lateral surface area of a sphere can be expressed as
A = 4 π r2 (13)
Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.
Calculate area of intersecting circles
Convert between units of area.
The controid of square, rectangle, circle, semi-circle and right-angled triangle.
The equation for a circle
Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.
Circumferences and areas of circles with diameters in inches.
Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.
Volume in US gallons and liters.
Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.
Radius and side lengths of equal areas, circles and squares.
The laws of fractional and integer exponents.
The product of all positive integers.
Distances between corners for hexagons and squares.
Calculate oblique triangles.
Verifying square corners.
Right angled triangle equations.
The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).
A rectangle is square if the lengths of both diagonals are equal.
Sine, cosine and tangent - the natural trigonometric functions.
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