Engineering ToolBox - Resources, Tools and Basic Information for Engineering and Design of Technical Applications!

This is an AMP page - Open full page! for all features.

Geometric Shapes - Areas

Sponsored Links



The area of a square can be calculated as

A = a2                            (1a)

The side of a square can be calculated as

a = A1/2                            (1b)

The diagonal of a square can be calculated as

d = a 21/2                        (1c)


The area of a rectangle can be calculated as

A = a b          (2a)

The diagonal of a rectangle can be calculated as

d = (a2 + b2)1/2     (2b)



The area of a parallelogram can be calculated as

A = a h

  = 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)

Equilateral Triangle

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

  = 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)


C = circumference


Sector and Segment of a Circle

Sector of Circle

Area of a sector of circle can be expressed as

A = 1/2 θr r2                            (9)

= 1/360 θd π r2


θr = angle in radians

θd = angle in degrees

Segment of Circle

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)

Right Circular Cylinder

Lateral surface area of a right circular circle can be expressed as

A = 2 π r h                                      (11)


h= height of cylinder (m, ft)

r = radius of base (m, ft)

Right Circular Cone

Lateral surface area of a right circular cone can be expressed as

A = π r l

= π r (r2 + h2)1/2                                   (12)


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)

Sponsored Links

Related Topics


Mathematical rules and laws - numbers, areas, volumes, exponents, trigonometric functions and more.

Related Documents

Area of Intersecting Circles

Calculate area of intersecting circles

Area Units Converter

Convert between units of area.

Centroids of Plane Areas

The controid of square, rectangle, circle, semi-circle and right-angled triangle.

Circle - the Chord Lengths when Divided in to Equal Segments

Calculate chord lengths when dividing the circumference of a circle into an equal number of segments.

Circle Equation

The equation for a circle

Circles - Circumferences and Areas

Circumferences and areas of circles with diameters in inches.

Circles Outside a Circle

Calculate the numbers of circles on the outside of an inner circle - like the geometry of rollers on a shaft.

Cylindrical Tanks - Volumes

Volume in US gallons and liters.

Elementary Curves

Ellipse, circle, hyperbola, parabola, parallel, intersecting and coincident lines.

Equal Areas - Circles vs. Squares

Radius and side lengths of equal areas, circles and squares.

Exponents - Powers and Roots

The laws of fractional and integer exponents.


The product of all positive integers.

Hexagons and Squares - Diagonal Lengths

Distances between corners for hexagons and squares.

Oblique Triangle

Calculate oblique triangles.

Pythagorean Theorem

Verifying square corners.

Right Angled Triangle

Right angled triangle equations.

Smaller Rectangles within a Larger Rectangle

The maximum number of smaller rectangles - or squares - within a larger rectangle (or square).

Squaring with Diagonal Measurements

A rectangle is square if the lengths of both diagonals are equal.

Trigonometric Functions

Sine, cosine and tangent - the natural trigonometric functions.

Sponsored Links

Search Engineering ToolBox

  • the most efficient way to navigate the Engineering ToolBox!

SketchUp Extension - Online 3D modeling!

Add standard and customized parametric components - like flange beams, lumbers, piping, stairs and more - to your Sketchup model with the Engineering ToolBox - SketchUp Extension - enabled for use with the amazing, fun and free SketchUp Make and SketchUp Pro . Add the Engineering ToolBox extension to your SketchUp from the Sketchup Extension Warehouse!


We don't collect information from our users. Only emails and answers are saved in our archive. Cookies are only used in the browser to improve user experience.

Some of our calculators and applications let you save application data to your local computer. These applications will - due to browser restrictions - send data between your browser and our server. We don't save this data.

Google use cookies for serving our ads and handling visitor statistics. Please read Google Privacy & Terms for more information about how you can control adserving and the information collected.

AddThis use cookies for handling links to social media. Please read AddThis Privacy for more information.