bartleby

Concept explainers

Question
Book Icon
Chapter 12, Problem 12.1P
To determine

The area enclosed within polygon ABDFGA.

Expert Solution & Answer
Check Mark

Answer to Problem 12.1P

The area enclosed within polygon ABDFGA is AABFDGA=280842.66ft2

Explanation of Solution

Given:

A closed polygon ABDFGA

Concept Used:

The formula for area of a triangle is

  A=s(sa)(sb)(sc)     ....... (1)

The formula for semi-perimeter of triangle is

  s=a+b+c2     ....... (2)

Here, A is area of triangle and s is semi-perimeter of triangle and a,b,c are the three sides of the triangle.

The area of polygon ABDFGA can be calculated by considering smaller triangles which together form the polygon.

  AABFDGA=ADFG+ABDG+AABG     ....... (3)

Calculation:

Consider the triangle DFG

Substitute 219.1ft for a , 567.6ft for b , 588.7ft for c in formula (2)

  s=219.1+567.6+588.72=1375.42=687.7ft

Substitute 219.1ft for a , 567.6ft for b , 588.7ft for c , 687.7ft for s in formula (1)

  ADFG=687.7( 687.7219.1)( 687.7567.6)( 687.7588.7)=687.7×468.6×120.1×99=3831594230=61899.87ft2

Consider the triangle BDG

Substitute 298.3ft for a , 588.7ft for b , 551.8ft for c in formula (2)

  s=298.3+588.7+551.82=1438.82=719.40ft

Substitute 298.3ft for a , 588.7ft for b , 551.8ft for c , 719.40ft for s in formula (1)

  ABDG=719.40( 719.40298.3)( 719.40588.7)( 719.40551.8)=719.40×421.1×130.7×167.6=6635983183=81461.54ft2

Consider the triangle ABG

Substitute 536.6ft for a , 551.8f for b , 610.5ft for c in formula (2)

  s=536.6+551.8+610.52=1698.92=849.45ft

Substitute 536.6ft for a , 551.8f for b , 610.5ft for c

  849.45ft , for s in formula (1)

  AABG=849.45( 849.45536.6)( 849.45551.8)( 849.45610.5)=849.45×312.85×297.65×238.95=18901091350=137481.24ft2

Substitute 137481.24ft2 for AABG , 81461.54ft2 for ABDG , 61899.87ft2 for ADFG in the equation (3),

  AABFDGA=ADFG+ABDG+AABG=61899.87+81461.54+137481.24=280842.66ft2

Conclusion:

The area enclosed within polygon ABDFGA is AABFDGA=280842.66ft2

Want to see more full solutions like this?

Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!
Students have asked these similar questions
A project schedule has been updated. The activity placement of spread footing concretewas originally scheduled to begin as early as day 10. The activity duration is 4 days. The actualstart day was day 12. The original schedule had a calculated total float of 7 days for this activity.The recalculated total float for the activity, when updated, would be
In preparation for a public hearing, an engineer needs to estimate the travel time savings for a proposed highway bypass of a small city in a rural area. The existing highway goes through the downtown area for 4.1 miles between the points where the bypass will connect. (a) If the engineer anticipates a standard deviation of 7 mi/h and would like a 95% confidence of estimating the mean speed within ±4 mi/h, how many runs should a travel time study include? (Enter the minimum number of runs that achieves a 95% confidence level.) runs (b) If the engineer measures an average speed of 34.9 mi/h through the town and the bypass is expected to operate at speeds of 65 mi/h over a distance of 6.2 miles, what is the expected travel time saving (in minutes) per vehicle? minutes Need Help? Read It Watch It
follow the instructions and make sure to right the complete solution
Knowledge Booster
Background pattern image
Civil Engineering
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, civil-engineering and related others by exploring similar questions and additional content below.
Similar questions
SEE MORE QUESTIONS
Recommended textbooks for you
Text book image
Structural Analysis
Civil Engineering
ISBN:9781337630931
Author:KASSIMALI, Aslam.
Publisher:Cengage,
Text book image
Structural Analysis (10th Edition)
Civil Engineering
ISBN:9780134610672
Author:Russell C. Hibbeler
Publisher:PEARSON
Text book image
Principles of Foundation Engineering (MindTap Cou...
Civil Engineering
ISBN:9781337705028
Author:Braja M. Das, Nagaratnam Sivakugan
Publisher:Cengage Learning
Text book image
Fundamentals of Structural Analysis
Civil Engineering
ISBN:9780073398006
Author:Kenneth M. Leet Emeritus, Chia-Ming Uang, Joel Lanning
Publisher:McGraw-Hill Education
Text book image
Sustainable Energy
Civil Engineering
ISBN:9781337551663
Author:DUNLAP, Richard A.
Publisher:Cengage,
Text book image
Traffic and Highway Engineering
Civil Engineering
ISBN:9781305156241
Author:Garber, Nicholas J.
Publisher:Cengage Learning