Trapezoidal area

Trapezoid (in North American English), or trapezium (in British English), is a convex quadrilateral with two sides parallel and two sides not.

Properties of a Trapezoid:

The sum of angles at vertices A and D, as well as B and C, is 180°.
The sum of adjacent angles in a trapezoid is 180°.
Generally, a trapezoid does not have an inscribed or circumscribed circle. However, it is possible to draw an ellipse around and inside any trapezoid.

Perimeter of Trapezoid

$$C=a+b+c+d$$

where,

a, b, c, d — lengths of the trapezoid sides.

Area of trapezoid via two bases and height:

$$S=\frac{a+b}{2} \times h$$

where,

a, b— lengths of the trapezoid bases.
h— height of the trapezoid.

Area of trapezoid via midline and height:

$$S=k \times h$$

where,

k— midline of the trapezoid.
h— height of the trapezoid.