One trapezium

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

Result

A =  1633.864 m2

Solution:

a=24 m b=36 m c=80 m d=80 m  x=ca=8024=56 m  s=x+b+d2=56+36+802=86 m  S1=s (sx) (sb) (sd)=86 (8656) (8636) (8680)=60 215 m2879.7727 m2  S1=xh/2  h=2 S1/x=2 879.7727/5631.4205 m  A=a+c2 h=24+802 31.42051633.8636=1633.864 m2a = 24 \ m \ \\ b = 36 \ m \ \\ c = 80 \ m \ \\ d = 80 \ m \ \\ \ \\ x = c-a = 80-24 = 56 \ m \ \\ \ \\ s = \dfrac{ x+b+d }{ 2 } = \dfrac{ 56+36+80 }{ 2 } = 86 \ 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) } = 60 \ \sqrt{ 215 } \ m^2 \doteq 879.7727 \ m^2 \ \\ \ \\ S_{ 1 } = xh/2 \ \\ \ \\ h = 2 \cdot \ S_{ 1 }/x = 2 \cdot \ 879.7727/56 \doteq 31.4205 \ m \ \\ \ \\ A = \dfrac{ a+c }{ 2 } \cdot \ h = \dfrac{ 24+80 }{ 2 } \cdot \ 31.4205 \doteq 1633.8636 = 1633.864 \ m^2



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