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 = sqrt [ 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*Pi*r
Area = Pi*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)* Pi * r 3
Surface Area = 4 * Pi * r 2

Volume and Surface Area of a Right Circular Cylinder

circular cylinder

Volume = Pi * r 2 * h
Surface Area = 2 * Pi * r * h

Volume and Surface Area of a Right Circular Cone

right cone

Volume = (1/3)* Pi * r 2 * h
Surface Area = Pi * r * sqrt (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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