Land - isosceles trapezoid

Calculate the content and perimeter of the building plot in the form of an isosceles trapezoid with bases 120m, 95m and height 50m.

Result

S =  5375 m2
o =  318.078 m

Solution:

a=120 c=95 h=50 S=(a+c)/2⋅ h=(120+95)/2⋅ 50=5375=5375 m2a = 120 \ \\ c = 95 \ \\ h = 50 \ \\ S = (a+c)/2 \cdot \ h = (120+95)/2 \cdot \ 50 = 5375 = 5375 \ m^2
x=(a−c)/2=(120−95)/2=252=12.5 b=h2+x2=502+12.52≐51.5388 o=a+c+2b=120+95+2⋅ 51.5388≐318.0776=318.078  m x = (a-c)/2 = (120-95)/2 = \dfrac{ 25 }{ 2 } = 12.5 \ \\ b = \sqrt{ h^2+x^2 } = \sqrt{ 50^2+12.5^2 } \doteq 51.5388 \ \\ o = a+c+2b = 120+95+2 \cdot \ 51.5388 \doteq 318.0776 = 318.078 \ \text{ m }

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