One trapezium

One trapezium has AB=24M, BC=36M, CD=80M, DA=80M long sides. Find the area.

Correct result:

A =  1633.864 m2

Solution:

a=24 m b=36 m c=80 m d=80 m  x=c−a=80−24=56 m  s=x+b+d2=56+36+802=86 m  S1=s⋅ (s−x)⋅ (s−b)⋅ (s−d)=86⋅ (86−56)⋅ (86−36)⋅ (86−80)≐60 215 m2≐879.7727 m2  S1=xh/2  h=2⋅ S1/x=2⋅ 879.7727/56≐31.4205 m  A=a+c2⋅ h=24+802⋅ 31.4205=1633.864 m2a=24 \ \text{m} \ \\ b=36 \ \text{m} \ \\ c=80 \ \text{m} \ \\ d=80 \ \text{m} \ \\ \ \\ x=c-a=80-24=56 \ \text{m} \ \\ \ \\ s=\dfrac{ x+b+d }{ 2 }=\dfrac{ 56+36+80 }{ 2 }=86 \ \text{m} \ \\ \ \\ S_{1}=\sqrt{ s \cdot \ (s-x) \cdot \ (s-b) \cdot \ (s-d) }=\sqrt{ 86 \cdot \ (86-56) \cdot \ (86-36) \cdot \ (86-80) } \doteq 60 \ \sqrt{ 215 } \ \text{m}^2 \doteq 879.7727 \ \text{m}^2 \ \\ \ \\ S_{1}=xh/2 \ \\ \ \\ h=2 \cdot \ S_{1}/x=2 \cdot \ 879.7727/56 \doteq 31.4205 \ \text{m} \ \\ \ \\ A=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 24+80 }{ 2 } \cdot \ 31.4205=1633.864 \ \text{m}^2

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