# Isosceles

Isosceles trapezium ABCD ABC = 12 angle ABC = 40 ° b=6. Calculate the circumference and area.

Result

o =  26.807
S =  28.554

#### Solution:

$a=12 \ \\ b=6 \ \\ B=40 \ ^\circ \ \\ \ \\ x=b \cdot \ \cos ( B ^\circ \rightarrow\ \text{rad})=b \cdot \ \cos ( B ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=6 \cdot \ \cos ( 40 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=4.59627 \ \\ c=a - 2 \cdot \ x=12 - 2 \cdot \ 4.5963 \doteq 2.8075 \ \\ \ \\ o=a + 2 \cdot \ b + c=12 + 2 \cdot \ 6 + 2.8075 \doteq 26.8075 \doteq 26.807$
$h=b \cdot \ \sin( B ^\circ \rightarrow\ \text{rad})=b \cdot \ \sin( B ^\circ \cdot \ \dfrac{ \pi }{ 180 } \ )=6 \cdot \ \sin( 40 ^\circ \cdot \ \dfrac{ 3.1415926 }{ 180 } \ )=3.85673 \ \\ S=\dfrac{ a+c }{ 2 } \cdot \ h=\dfrac{ 12+2.8075 }{ 2 } \cdot \ 3.8567 \doteq 28.5542 \doteq 28.554$

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