# 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 = 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

## 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)