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 =  1414.5937

Solution:

$$\begin{gathered} a=40.5 \\ b=42.5 \\ c=52.8 \\ d=35.0 \\ x=c-a=52.8-40.5={\displaystyle \frac{123}{10}}=12.3 \\ s=(b+d+x)\mathrm{/}2=(42.5+35+12.3)\mathrm{/}2={\displaystyle \frac{449}{10}}=44.9 \\ {S}_1=\sqrt{s\cdot (s-b)\cdot (s-d)\cdot (s-x)}=\sqrt{44.9\cdot (44.9-42.5)\cdot (44.9-35)\cdot (44.9-12.3)}\doteq 186.4898 \\ h=2\cdot S_1\mathrm{/}x=2\cdot 186.4898\mathrm{/}12.3\doteq 30.3236 \\ {S}_2=a\cdot h=40.5\cdot 30.3236\doteq 1228.1039 \\ S=S_1+S_2=186.4898+1228.1039=1414.5937 \end{gathered}$$

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