# Trapezoid

## 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`

## See also

Plane Geometry calculators

Geometry calculators

Mathematics calculators