# Four sides of trapezoid

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

Result

S =  1414.594

#### Solution:

$a = 40.5 \ \\ b = 42.5 \ \\ c = 52.8 \ \\ d = 35.0 \ \\ \ \\ x = c-a = 52.8-40.5 = \dfrac{ 123 }{ 10 } = 12.3 \ \\ s = (b+d+x)/2 = (42.5+35+12.3)/2 = \dfrac{ 449 }{ 10 } = 44.9 \ \\ S_{ 1 } = \sqrt{ s \cdot \ (s-b) \cdot \ (s-d) \cdot \ (s-x) } = \sqrt{ 44.9 \cdot \ (44.9-42.5) \cdot \ (44.9-35) \cdot \ (44.9-12.3) } \doteq 186.4898 \ \\ h = 2 \cdot \ S_{ 1 }/x = 2 \cdot \ 186.4898/12.3 \doteq 30.3236 \ \\ S_{ 2 } = a \cdot \ h = 40.5 \cdot \ 30.3236 \doteq 1228.1039 \ \\ S = S_{ 1 }+S_{ 2 } = 186.4898+1228.1039 \doteq 1414.5937 = 1414.594$

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