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

Right Triangle

Area and Perimeter of Triangle



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


Rectangle

Perimeter = 2L + 2W
Area = L W

Area of Parallelogram


Parallelogram

Area = b h

Area of Trapezoid


Trapezoid

Area = (1 / 2)(a + b) h

Circumference of a Circle and Area of a Circular Region


Circle

Circumference = 2 π r
Area = π r 2

Arclength and Area of a Circular Sector

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


Sector

Volume = L*W*H
Surface Area = 2(L W + H W + H L)

Volume and Surface Area of a Sphere

Sphere

Volume = (4/3) π r 3
Surface Area = 4 π r 2

Volume and Surface Area of a Right Circular Cylinder

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

right 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.





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