Two lines, parallel to the bases of a trapezoid divide each leg into three congruent parts and divide the trapezoid into three parts as well. Find the area of the middle part if the top and bottom parts have area S1 and S3.

S2 = (S1+S3) / 2

Step-by-step explanation:

The area of a trapezoid is the product of the midline length and the height. The parallel lines have divided the height into three equal pieces, so the midline of the middle piece will be the average of the midline lengths of the top and bottom pieces.

The result is that the area of the middle part is the average of the areas of the top and bottom parts:

S2 = (S1+S3) / 2