Trapezoid 16783

The garden, in the shape of an isosceles trapezoid, has a base length of 44 m and 16 meters. The arms are 25 m long. 1/5 of the area is for a road and a cottage. How many m² of the area will be left for planting trees?

Correct answer:

S =  497.0956 m²

Step-by-step explanation:

$$\begin{gathered} a=44\text{m} \\ c=16\text{m} \\ r=25\text{m} \\ q=1-\frac{1}{5}=\frac{1\cdot 5}{5}-\frac{1}{5}=\frac{5}{5}-\frac{1}{5}=\frac{5-1}{5}=\frac{4}{5}=0.8 \\ h=\sqrt{r^2-((a-c)/2{)}^2}=\sqrt{25^2-((44-16)/2{)}^2}=\sqrt{429}\text{m}\doteq 20.7123\text{m} \\ {S}_1=\frac{a+c}{2}\cdot h=\frac{44+16}{2}\cdot 20.7123=30\sqrt{429}{\text{m}}^2\doteq 621.3695{\text{m}}^2 \\ S=q\cdot S_1=0.8\cdot 621.3695=24\sqrt{429}=497.0956{\text{m}}^2 \end{gathered}$$

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