Surveyor

Calculate the area of ​​what may vary rectangular, if it focused by surveyor and found the dimensions 18 x 15 m while in each of the four joint points can be position deviation 25 cm?

Correct result:

ΔS =  23.3 m²

Solution:

$$\begin{gathered} 25^2=c^2+c^2 \\ c={\displaystyle \frac{25}{100\cdot \sqrt{2}}}=0.177m \\ S=ab=270m^2 \\ {S}_1=(a+c)(b+c)=281.79m^2 \\ {S}_2=(a-c)(b-c)=258.46m^2 \\ \mathrm{\Delta }S=S_1-S_2=23.3{\text{m}}^2 \end{gathered}$$

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