Making Connection Between Areas of Trapezoids and Parallelograms

Our last two discussions was about deriving the areas of trapezoids and parallelograms. In this post, we relate the two areas. We derive the area of a trapezoid using the area of a parallelogram. In the following derivation, we use the trapezoid with bases $latex b_1$ and $latex b_2$ and altitude $latex h$.

area of trapezoid

To form a parallelogram using a trapezoid, make a copy of a trapezoid and then rotate it 180 degrees and make the corresponding sides coincide as shown below. Continue reading

Derivation of the Area of a Trapezoid

A trapezoid (or trapezoid) is a quadrilateral with exactly one pair* of parallel sides. In the figure below, ABCD is a trapezoid and AB is parallel to CD.

area of a trapezoid

In this post, we derive the area of a trapezoid. We use the fact that a trapezoid can be partitioned into two triangles and one rectangle. The area $latex A$ of a trapezoid is equal to the sum of the areas $latex A_1, A_3$ of the two triangles and the area $latex A_2$ of the rectangle. Continue reading