Isosceles trapezoid

The old father decided to change the top plate of an isosceles-like trapezoid, which has basic dimensions of 120 cm and 60 cm, and a shoulder that is 50 centimeters long. How much does it pay for a new plate and a square meter worth 17 euros?

Correct answer:

x =  6.12 Eur

Step-by-step explanation:

$$\begin{gathered} a=120\text{cm}\to \text{m}=120:100\text{m}=1.2\text{m} \\ c=60\text{cm}\to \text{m}=60:100\text{m}=0.6\text{m} \\ r=50\text{cm}\to \text{m}=50:100\text{m}=0.5\text{m} \\ h=\sqrt{r^2-((c-a)/2{)}^2}=\sqrt{0.5^2-((0.6-1.2)/2{)}^2}=\frac{2}{5}=0.4\text{m} \\ S=(a+c)\cdot h/2=(1.2+0.6)\cdot 0.4/2=\frac{9}{25}=0.36{\text{m}}^2 \\ x=17\cdot S=17\cdot 0.36=6.12\text{Eur} \end{gathered}$$

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