# 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:

$a=24 \ \text{m} \ \\ b=36 \ \text{m} \ \\ c=80 \ \text{m} \ \\ d=80 \ \text{m} \ \\ \ \\ x=c-a=80-24=56 \ \text{m} \ \\ \ \\ s=\dfrac{ x+b+d }{ 2 }=\dfrac{ 56+36+80 }{ 2 }=86 \ \text{m} \ \\ \ \\ S_{1}=\sqrt{ s \cdot \ (s-x) \cdot \ (s-b) \cdot \ (s-d) }=\sqrt{ 86 \cdot \ (86-56) \cdot \ (86-36) \cdot \ (86-80) } \doteq 60 \ \sqrt{ 215 } \ \text{m}^2 \doteq 879.7727 \ \text{m}^2 \ \\ \ \\ S_{1}=xh/2 \ \\ \ \\ h=2 \cdot \ S_{1}/x=2 \cdot \ 879.7727/56 \doteq 31.4205 \ \text{m} \ \\ \ \\ A=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 24+80 }{ 2 } \cdot \ 31.4205=1633.864 \ \text{m}^2$

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