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
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.
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