Garden G

The rectangular trapezoidal garden has a base length of 81m, 76m, and a vertical arm of 12m. Calculate how many m² of area will remain for planting greenery, if 1/3 of the area is built. Calculate the consumption of mesh for land fencing.

Correct result:

S =  1256 m²
o =  106 m

Solution:

$$\begin{gathered} a=81\text{ m } \\ c=76\text{ m } \\ d=12\text{ m } \\ {S}_1={\displaystyle \frac{a+c}{2}}\cdot d={\displaystyle \frac{81+76}{2}}\cdot 12=942{\text{m}}^2 \\ S=S_1+{\displaystyle \frac{1}{3}}\cdot S_1=942+{\displaystyle \frac{1}{3}}\cdot 942=1256{\text{m}}^2 \end{gathered}$$

$$\begin{gathered} c=\sqrt{d^2+(a-c{)}^2}=\sqrt{12^2+(81-13{)}^2}=13\text{ m } \\ o=a+b+c+d=81+b+13+12=106\text{ m} \end{gathered}$$

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