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Measuring Distances, Angles and Areas. AGME 1613 Fundamentals of Agricultural Systems Technology. Objectives. Describe the advantages and disadvantages of four methods of measuring distance. Use each of the four methods in a simulated survey. Determine the area of standard geometric shapes.

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Measuring distances angles and areas

Measuring Distances, Angles and Areas

AGME 1613

Fundamentals of Agricultural Systems Technology


Objectives
Objectives

  • Describe the advantages and disadvantages of four methods of measuring distance.

  • Use each of the four methods in a simulated survey.

  • Determine the area of standard geometric shapes.

  • Determine the area of irregularly shaped fields.


Common units of distance
Common Units of Distance

  • Feet

  • Yards

  • Rods (16.5-ft.)

  • Chain (88-ft.)

  • Mile (5280-ft.)

  • Meters (.3084-ft.)

  • Kilometers (.6214 miles)


Four methods of measuring distance
Four Methods of Measuring Distance

  • Pacing

  • Odometer wheel

  • Taping

  • Stadia Method


Pacing
Pacing

  • Simplest and easiest method of determining distances.

  • Requires only one person.

  • D = Pace factor x # of paces

  • With practice, accuracy of

    + 2% is possible.

  • Measures “surface distance.”


Odometer wheel
Odometer Wheel

  • Mechanical device for measuring distance.

    • Direct reading or

    • Revolution counting

  • D = # Rev x Circumference

  • Only one person required.

  • Accuracy of + 1%.

  • Measures “surface distance.”

Determine the distance if the wheel makes 200.5 revolutions.


Stadia method
Stadia Method

  • Very quick method of determining distance.

  • D = (TSR – BSR) x 100

  • More accurate than chaining.

  • Requires “leveling equipment.”

  • Requires two people.

  • What is the distance from the level to the rod in this example?


Taping
Taping

  • Most accurate method of determining distance.

  • Accuracy + .03 %.

  • Requires:

    • Specialized equipment

    • Minimum of two surveyors

    • Skill

  • Equipment:

    • 100-ft. steel tape,

    • chaining pins,

    • range poles,

    • plumb bobs,

    • hand level


Additional methods
Additional methods

  • Optical range finders

  • Electronic distance measurement

  • Global Positioning System (GPS) receivers


Determining land areas
Determining Land Areas

  • Why would you need to be able to determine land areas?

  • How is land area typically expressed?


Standard geometric shapes
Standard Geometric Shapes

  • Square

  • Rectangle

  • Parallelogram

  • Trapezoid

  • Triangle

  • Circle

  • Sector


Square and rectangle
Square and Rectangle

  • Formula

    • A (ft2) = B’ x H’

    • A (ac) = B’ x H’

43,560

250-ft.

750-ft


Parallelogram
Parallelogram

  • Formula

    • A (ft2) = B’ x H’

    • A (ac) = B’ x H’

43,560

H

B

What is the area (ft2), if the Base = 1200-ft and the Height = 300-ft?


Trapezoid

What is the area of the trapezoid below?

700-ft.

375-ft.

300-ft.

Trapezoid

  • Formula

    • A (ft2) = H x [(a+b)/2]

A

H

B


Triangle

400-ft.

325-ft.

Triangle

  • A (ft2) = ½ x B x H

  • What is the acreage of the field at left?

H

B


Circle

600-ft.

Circle

  • A (ft2) = pi x r2

  • A chemical needs to be applied to this field at a rate of 3.0-lbs/ac. How much chemical should be applied?

r


Sector

600-ft.

Sector

  • A (ft2) = pi x r2 x O

360



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