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:

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

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Pythagorean theorem is the base for the right triangle calculator. Do you want to convert length units? See also our trigonometric triangle calculator.

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