How is the area of trapizoid related to the area of a parrellogram?

Answer 1

The area of a trapezoid can be related to the area of a parallelogram by considering that both shapes have a base and height. The area of a trapezoid is calculated using the formula (A = \frac{1}{2} (b_1 + b_2) h), where (b_1) and (b_2) are the lengths of the two parallel bases and (h) is the height. In contrast, the area of a parallelogram is given by (A = b \cdot h), where (b) is the length of one base and (h) is the height. If you take a trapezoid and extend it into a parallelogram by duplicating one of its bases, the relationship between the areas is evident: the trapezoid's area is essentially half of the area formed by the parallelogram that encompasses it.