How can we calculate the area of ​​a trapezoid?

The application allows to reach the formula of the area of ​​a trapezium using the construction of a parallelogram with the same height.

What is the relationship between the area of the trapezium and the area of the quadrilateral [AD’A’D]?

The area of the trapezium is half the area of the quadrilateral.

Since the quadrilateral [AD’A’D] is a parallelogram, what formula do we obtain to calculate the area of the trapezium?

The area of the parallelogram is given by \(\overline{AD’} \times h\), where \(h\), which is the height of the trapezium, is also the height of [AD’A’D] relative to the side [AD’]. Then the area of the trapezium is given by $${\overline{AD’} \times h \over 2} = {(b_1 + b_2) \times h \over 2},$$that is, it is half the product of the sum of the lengths of the bases by the height.