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Math in the Workplace: Overview

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Math in the Work Place

Math in the Workplace - Geometry

IDAHO FARM OWNER

Livestock & Crops Production
Owner / Manager

 

 Job Description: Operate farms, ranches, greenhouses, nurseries, timber tracts, or other agricultural production establishments which produce crops, horticultural specialties, livestock, poultry, finfish, shellfish, or animal specialties. May plant, cultivate, harvest, perform post-harvest activities, and market crops and livestock; may hire, train, and supervise farm workers or supervise a farm labor contractor; may prepare cost, production, and other records. May maintain and operate machinery and perform physical work.
   


Problem:

Betsy is tethered to the barn at one corner by a 100 ft rope. A fence keeps her out of the garden. Find, to the nearest square foot, the area in which Betsy can graze.

diagram

Area of triangle = base x height

2
Area of circle = pr2
Area of sector = Area of circle x  sector angle 360°

solution

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Solution:  

Break the diagram into 4 different areas. Begin with exact values and calculate the approximation at the end.

1. Area of Section I is contained in a right isosceles triangle.

    Area of Section I:
    25 ft x 25 ft

    2     		= 312.50 ft2

2. Area of Section II is contained in a sector of a circle with a sector angle of 45°, a radius of 100 ft - diagonal of Section I isosceles triangle:

    100 ft - (252 ft2 + 252 ft2) = 100 ft - 1250 ft2

    100 ft - 35.3553 ft = 64.6447 ft

    Area of Section II:
    p (64.6447 ft)2

    360°/45°    		 = 13128.5 ft2

    8    		 = 1,641.1 ft2

3. Area of section III is contained in a sector of a circle with a sector angle of 225° and a radius of 100 ft.

    Area of Section III:
    p (100 ft)2

    360°/225°    		 = 19,635 ft2

4. Area of Section IV is contained in a sector of a circle with a sector angle of 90° and a radius of 100 ft - 80 ft = 20 ft.

    Area of Section IV:
    p (20 ft)2

    360°/90°    		 = 1,256.64 ft2

    4    		 = 314.16 ft2

5. Area in which Betsy can graze = sum of areas of Sections I - IV

    (312.50 + 1,641.1 + 19,635 + 314.16) ft2 = 21,903 ft2