Area Calculations

Course Number
This is an essential course for the technician or professional who needs to understand the basic theory and computational techniques that are used to compute area using field measurements or a map.  The course begins with a discussion of how area is determined from horizontal linear measurements.  The rest of the program covers the techniques used in the field and with a map.  Field techniques discussed include dividing a tract into simple geometric shapes such as triangles, rectangles and trapezoids, and computing the individual areas.  For tracts with irregular boundaries, the concept of constructing offsets to a line is shown where a series of trapezoids and triangles are constructed and computed.  Emphasis is placed on determining area from coordinates and the double meridian distance (DMD) methods.  Examples are worked to illustrate the latter two methods.  The course closes with a discussion of the methods that can be used with a map, including breakdown into simple geometric shapes, counting grid squares on an overlay, digitizing coordinates and use of a planimeter (a mechanical numerical integrator).

Suggested Prerequisites:
Basic analytic geometry, coordinate geometry and triangle solving skills are developed in this course.  The learner must be familiar with equations for lines, curves, and the trigonometric functions.  If the learner does not have prior coursework in traverse computations or if the practical experience in such computations is limited, Traverse Computations I and Traverse Computations II are highly recommended before taking this course.
Learners who successfully complete this course will receive a certificate of completion for 1 professional development hour.
More Information...

Joseph V.R. Paiva is CEO of GeoLearn, LLC (, which is launching an online professional education business for the geospatial industry in early 2014. Joe started this business with his partner Bob Morris, whose most recent global industry position was President of Leica Mapping. Previously, Dr. Paiva was CTO of SADAR 3D and COO of Gatewing NV, a Belgian unmanned airborne systems company. Prior engagements in consulting were in the field of geomatics and general business, particularly to international developers, manufacturers and distributors of instrumentation and other geomatics tools. Dr. Paiva and Mr. Morris continue to be involved in consultancy through a separate partnership called GeoSpatial Associates, LLC will continue this consultancy. Joe’s career includes: managing director of Spatial Data Research, Inc., a GIS data collection, compilation and software development company; various assignments at Trimble Navigation Ltd. including senior scientist and technical advisor for Land Survey research & development, VP of the Land Survey group, and director of business development for the Engineering and Construction Division; vice president and a founder of Sokkia Technology, Inc., guiding development of GPS- and software-based products for surveying, mapping, measurement and positioning. He has also held senior technical management positions in The Lietz Co. and Sokkia Co. Ltd. Prior to that was assistant professor of civil engineering at the University of Missouri-Columbia, and a partner in a surveying/civil engineering consulting firm. He has continued his interest in teaching by serving as an adjunct instructor for online course development and teaching at the Missouri University of Science and Technology. His key contributions in the development field are: design of software flow for the SDR2, SDR20 series and SDR33 Electronic Field Books and software interface for the Trimble TTS500 total station. He is a registered Professional Engineer and Professional Land Surveyor, has served as ACSM representative to the Accrediting Board for Engineering and Technology (ABET), serving as a program evaluator, team chair, and commissioner and has more than 30 years experience working in civil engineering, surveying and mapping. He writes for POB, GeoDataPoint and The Empire State Surveyor magazines and has been a past contributor of columns to Civil Engineering News. Joe has also been a consultant to the Geomatics Industry Association of America, later reorganized under the Association of Equipment Manufacturers (AEM) as the Geospatial Industry Group, Joe has organized and presented workshops and authored and edited articles for the technical press in this role.

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