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I want to know if I did this one right, could anyone solve this one so I can double check my answers?

Thank you in advance!

 

A company buys an industrial plot with the dimensions according to the figure below. What does the land cost if the land costs 500 SEK / sec (Round to the nearest thousand SEK.)

SEK = A currency in Sweden

 

Guest Jun 9, 2017
 #1
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A company buys an industrial plot with the dimensions according to the figure below. What does the land cost if the land costs 500 SEK / sec (Round to the nearest thousand SEK.)

SEK = A currency in Sweden

\(It \ is \ certainly \ 500 \ SEK / m ^ 2.\)

 

4 points starting at the left bottom counterclockwise A, B, C, D.

 

Parallel to  \(\overline{AB}\)  through D to new point E.

Rectangle over A to new point G

Rectangle over B to new point H

Rectangle over E to new point F

 

\(\overline{AB}=a=81.9\\ \overline{AD}=b=62.2\\ \overline{BC}=c=73.4\\ ∠DAG=\alpha=4.9°\\ ∠EBH=∠CEF=\beta=8.2°\\ \overline{DG}=d=b\ sin4.9°=62.2\ sin4.9°=5.3129\\ \overline{AG}=h=b\ cos4.9°=62.2\ cos4.9°=61.9727\\ \overline{EH}=e =h\ tan8.2°=62.2\ cos4.9°\ tan8.2°=8.9304\)

\(\overline{BE}=f=h/cos8.2°=62.2\ cos4.9°/cos8.2°=62.6128\\ \overline{CE}=g=73.4-f=73.4-62.2\ cos4.9°/cos8.2°=10.7872\\ \overline{EF}=k=g\ cos8.2°=(73.4-62.2\ cos4.9°/cos8.2°)\cdot cos8.2°=10.6769 \\ \overline{CF}=l=g\ sin8.2°=(73.4-62.2\ cos4.9°/cos8.2°)\cdot sin8.2°=1.5386\)


 \(\large A_{trapeze}=\frac{a+(a+d+e)}{2}\times h\)

 

\(a=81.9\\ d=62.2sin4.9°\\ h=62.2cos4.9°\\ e=h\ tan8.2°=62.2cos4.9°\times tan 8.2°\)

 

\(\large A_{trapeze}=\frac{81.9+(81.9+62.2 sin4.9+62.2 cos4.9° tan 8,2°)}{2}\times 62.2cos4.9°\)

 

\(\large A_{trapeze}=5516.91098632\ m^2\)

 

 

\(\large {\color{blue} A_{small \ triangle}=\frac{1}{2}\cdot k\cdot l}=\frac{1}{2}\cdot 10.6769\cdot 1.5386 \)

 

\(\large A_{small \ triangle}=8.2137\ m^2\) 

 

 

\(\large A_{large \ triangle}=\frac{1}{2}\cdot (d+a+e) \cdot k\)

 

\(\large A_{large \ triangle}=\frac{1}{2}\cdot (5.3129+81.9+8.9304) \cdot 10.6769\)

 

\(\large A_{large \ triangle}=513.2562\ m^2\)

 

 

\(\large A_{company}=A_{trapeze}+A_{small\ triangel}+A_{large\ triangle}\)

 

\(\large A_{company}=5516.9110\ m^2+8.2137\ m^2 + 513.2562\ m^2\)

 

\(\large A_{company}=6038.3809 \ m^2\)

 

 

\(\large purchase\ price=A_{company}\times 500\ SEK/m^2\\\large \)

.                                \(\large =6038.3809\ m^2\times 500\ SEK/m^2\)

 

\(\large purchase\ price≈3019\ thousand \ SEK\)

 

 

\(\large The \ buyer \ must \ pay \ 3019 \ thousand \ SEK \ for \ the \ company \ premises.\)

 

laugh  !

asinus  Jun 9, 2017
edited by asinus  Jun 9, 2017
edited by asinus  Jun 10, 2017
edited by asinus  Jun 10, 2017
 #2
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Thank you!

 

You corrected a lot of my mistakes haha :D

Guest Jun 9, 2017
 #3
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Use this online calculator to verify your answers:

https://rechneronline.de/pi/quadrilateral.php

Guest Jun 9, 2017

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