# Garden exchange

The garden has the shape of a rectangular trapezoid, the bases of which have dimensions of 60 m and 30 m and a vertical arm of 40 m. The owner exchanged this garden for a parallelogram, the area of which is 7/9 of the area of a trapezoidal garden. What is the size of the new garden in ares?

Correct result:

S2 =  14 a

#### Solution:

$a=60 \ \text{m} \ \\ c=30 \ \text{m} \ \\ d=40 \ \text{m} \ \\ \ \\ S_{1}=\dfrac{ a+c }{ 2 } \cdot \ d=\dfrac{ 60+30 }{ 2 } \cdot \ 40=1800 \ \text{m}^2 \ \\ S_{3}=\dfrac{ 7 }{ 9 } \cdot \ S_{1}=\dfrac{ 7 }{ 9 } \cdot \ 1800=1400 \ \text{m}^2 \ \\ \ \\ S_{2}=S_{3} \rightarrow a=S_{3} / 100 \ a=1400 / 100 \ a=14 \ a=14 \ \text{a}$

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