Isosceles trapezoid

The old father decided to change the top plate of an isosceles-like trapezoid with the basic dimensions of 120 cm and 60 cm, and the shoulder 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:

$$\begin{gathered} a=120\text{ cm}\to \text{ m}=120\mathrm{/}100\text{ m}=1.2\text{ m } \\ c=60\text{ cm}\to \text{ m}=60\mathrm{/}100\text{ m}=0.6\text{ m } \\ r=50\text{ cm}\to \text{ m}=50\mathrm{/}100\text{ m}=0.5\text{ m } \\ h=\sqrt{r^2-((c-a)\mathrm{/}2{)}^2}=\sqrt{0.5^2-((0.6-1.2)\mathrm{/}2{)}^2}={\displaystyle \frac{2}{5}}=0.4\text{ m } \\ S=(a+c)\cdot h\mathrm{/}2=(1.2+0.6)\cdot 0.4\mathrm{/}2={\displaystyle \frac{9}{25}}=0.36{\text{m}}^2 \\ x=17\cdot S=17\cdot 0.36={\displaystyle \frac{153}{25}}={\displaystyle \frac{153}{25}}\text{ Eur}=6.12\text{ Eur} \end{gathered}$$

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