Garden exchange

The garden has a rectangular trapezoid shape, 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, which is 7/9 of the area of a trapezoidal garden. What is the size of the new garden in ares?

Correct answer:

S₂ =  14 a

Step-by-step explanation:

$$\begin{gathered} a=60\text{m} \\ c=30\text{m} \\ d=40\text{m} \\ {S}_1=\frac{a+c}{2}\cdot d=\frac{60+30}{2}\cdot 40=1800{\text{m}}^2 \\ {S}_3=\frac{7}{9}\cdot S_1=\frac{7}{9}\cdot 1800=\frac{7\cdot 1800}{9}=\frac{12600}{9}=1400{\text{m}}^2 \\ {S}_2=S_3\to \text{a}=S_3:100\text{a}=1400:100\text{a}=14\text{a}=14\text{a} \end{gathered}$$

Try another example