A new patio will be an irregular hexagon. The patio will have two long parallel sides and an area of 360 square feet. The area of a geometrically similar patio is 250 square feet, and its long parallel sides are 12.5 feet apart. What is the corresponding distance on the new patio?

Given two similar figures, the ratio of any two corresponding sides measures with the equal in square to the ratio of any two corresponding area measure. Let x be the separation of the two long parallel sides in the larger patio.

x²/12.5 ² = 360/250

x / 12.5 = 6/5

x = (6*12.5) / 5

x = 75/5 = 15

That is the corresponding distance on the new patio.