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.

Step-by-step explanation:

Consider trapezoid ABCD. Let BC=a, AD=b and the height of trapezoid be h. Then segment

and trapezoids EBCF, GEFH, AGHD have the sqme height

The area of trapezoid EBCF is

the area of trapezoid GEFH is

the area of trapezoid AGHD is

Now,

Multiplying the second equation by 2 and subtracting the first equation, you get

Multiplying the first equation by 5 and subtracting the second equation, you get

Hence,