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?

Result

x =  6.12 Eur

Solution:

a=120 cm=120/100 m=1.2 m c=60 cm=60/100 m=0.6 m r=50 cm=50/100 m=0.5 m  h=r2−((c−a)/2)2=0.52−((0.6−1.2)/2)2=25=0.4 m  S=(a+c)⋅ h/2=(1.2+0.6)⋅ 0.4/2=925=0.36 m2  x=17⋅ S=17⋅ 0.36=15325=6.12 Eura=120 \ cm=120 / 100 \ m=1.2 \ m \ \\ c=60 \ cm=60 / 100 \ m=0.6 \ m \ \\ r=50 \ cm=50 / 100 \ m=0.5 \ m \ \\ \ \\ h=\sqrt{ r^2-((c-a)/2)^2 }=\sqrt{ 0.5^2-((0.6-1.2)/2)^2 }=\dfrac{ 2 }{ 5 }=0.4 \ \text{m} \ \\ \ \\ S=(a+c) \cdot \ h / 2=(1.2+0.6) \cdot \ 0.4 / 2=\dfrac{ 9 }{ 25 }=0.36 \ \text{m}^2 \ \\ \ \\ x=17 \cdot \ S=17 \cdot \ 0.36=\dfrac{ 153 }{ 25 }=6.12 \ \text{Eur}

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