Table of Formulas For Geometry
A table of formulas for geometry, related to area and perimeter of triangles, rectangles, cercles, sectors, and volume of sphere, cone, cylinder are presented.
Right Triangle and Pythagora's theorem
Pythagora's theorem: The two sides a and b of a right triangle and the hypotenuse c are related by
a 2 + b 2 = c 2
Area and Perimeter of Triangle
Perimeter = a + b + c
There are several formulas for the area.
If the base b and the corresponding height h are known, we use the formula
Area = (1 / 2) × b × h.
If two sides and the angle between them are known, we use one of the formulas, depending on which side and which angle are known
Area = (1 / 2) × b × c sin A
Area = (1 / 2) × a × c sin B
Area = (1 / 2) × a × b sin C .
If all three sides are known, we may use Heron's formula for the area.
Area = √ [ s(s - a)(s - b)(s - c) ] , where s = (a + b + c)/2.
Area and Perimeter of Rectangle
Perimeter = 2L + 2W
Area = L × W
Area of Parallelogram
Area = b × h
Area of Trapezoid
Area = (1 / 2)(a + b) × h
Circumference of a Circle and Area of a Circular Region
Circumference = 2 × π × r
Area = π × r 2
Arclength and Area of a Circular Sector
Arclength: s = r × t
Area = (1/2) × r 2 × t
where t is the central angle in RADIANS.
Volume and Surface Area of a Rectangular Solid
Volume = L*W*H
Surface Area = 2(L × W + H × W + H × L)
Volume and Surface Area of a Sphere
Volume = (4/3) × π × r 3
Surface Area = 4 × π × r 2
Volume and Surface Area of a Right Circular Cylinder
Volume = π × r 2 × h
Total Surface Area = 2 × π × r × h + 2 × π × r 2
Volume and Surface Area of a Right Circular Cone
Volume = (1/3) × π × r 2 × h
Surface Area = π × r × √ (r 2 + h 2)
See also area of regular polygons.
More References and Links to Geometry Geometry Tutorials, Problems and Interactive Applets.
Area, Perimeter and Diagonal of a Rectangle - Geometry Calculator.
Length and Width of Rectangle - Geometry Calculator.