Trapezoid

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Trapezoid formulas

Angles

Angles A and D and angles C and B are supplementary.

$A+D = 180°$

$C+B = 180°$

Height

$h=d*sin(A)=d*sin(D)=b*sin(B)=b*sin(C)$

Diagonals

$d_1=sqrt(a^2+b^2-2*a*b*cos(B))=sqrt(c^2+d^2-2*c*d*cos(D))$

$d_2=sqrt(a^2+d^2-2*a*d*cos(A))=sqrt(b^2+c^2-2*b*c*cos(C))$

$d_1^2+d_2^2 = b^2+d^2+2*a*c$

Median segment length

$m=(a+c)/2$

Area

$Ar=(a+c)/2*h = m*h$

Perimeter

$P = a+b+c+d$