Rectangular 61183

Mr. Nový exchanged his rectangular plot of 5.2 hectares with his neighbor for two. The first plot has the shape of a square with a side of 70 m, and the second has the shape of a rectangle with dimensions of 110 m and 410 m. After the exchange, does the new owner have a larger or smaller land area than before? By how many ares?

Correct answer:

w =  1
d =  20 a

Step-by-step explanation:

$$\begin{gathered} S=5.2\text{ha}\to {\text{m}}^2=5.2\cdot 10000{\text{m}}^2=52000{\text{m}}^2 \\ a=70\text{m} \\ x=110\text{m} \\ y=410\text{m} \\ {S}_1=a\cdot a=70\cdot 70=4900{\text{m}}^2 \\ {S}_2=x\cdot y=110\cdot 410=45100{\text{m}}^2 \\ {S}_3=S_1+S_2=4900+45100=50000{\text{m}}^2 \\ S>S_3 \\ w=1 \end{gathered}$$

$$\begin{gathered} d_1=S-S_3=52000-50000=2000{\text{m}}^2 \\ d=d_1/100=2000/100=20\text{a} \end{gathered}$$

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