+0

# I want to know if I did this one right

0
99
3

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
Sort:

### 3+0 Answers

#1
+6702
+1

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

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

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

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

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

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

$$\large A_{trapeze}=5516.91098632\ m^2$$

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

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

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

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

$$\large A_{large \ triangle}=513.2562\ m^2$$

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

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

$$\large A_{company}=6038.3809 \ m^2$$

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

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

$$\large purchase\ price≈3019\ thousand \ SEK$$

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

!

asinus  Jun 9, 2017
edited by asinus  Jun 9, 2017
edited by asinus  Jun 10, 2017
edited by asinus  Jun 10, 2017
#2
0

Thank you!

You corrected a lot of my mistakes haha :D

Guest Jun 9, 2017
#3
0

Use this online calculator to verify your answers:

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

Guest Jun 9, 2017

### 15 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details