# 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:

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

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