# Four sides of trapezoid

Trapezoid is given by length of four sides: 40.5 42.5 52.8 35.0. Calculate its area.

Correct result:

S =  1414.594

#### Solution:

$a=40.5 \ \\ b=42.5 \ \\ c=52.8 \ \\ d=35.0 \ \\ \ \\ x=c-a=52.8-40.5=\dfrac{ 123 }{ 10 }=12.3 \ \\ s=(b+d+x)/2=(42.5+35+12.3)/2=\dfrac{ 449 }{ 10 }=44.9 \ \\ S_{1}=\sqrt{ s \cdot \ (s-b) \cdot \ (s-d) \cdot \ (s-x) }=\sqrt{ 44.9 \cdot \ (44.9-42.5) \cdot \ (44.9-35) \cdot \ (44.9-12.3) } \doteq 186.4898 \ \\ h=2 \cdot \ S_{1}/x=2 \cdot \ 186.4898/12.3 \doteq 30.3236 \ \\ S_{2}=a \cdot \ h=40.5 \cdot \ 30.3236 \doteq 1228.1039 \ \\ S=S_{1}+S_{2}=186.4898+1228.1039=1414.594$

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