# 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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For Basic calculations in analytic geometry is helpful line slope calculator. From coordinates of two points in the plane it calculate slope, normal and parametric line equation(s), slope, directional angle, direction vector, the length of segment, intersections the coordinate axes etc. See also our trigonometric triangle calculator.

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