I need help calculating 17 equal trapazoid dimensions around a 25' diameter circle.

Question

I'm building a deck around an above ground, round swimming pool. The top rail of the pool consists of 17 equal length straight pieces that are 55" each to form the "circle". I want to frame 17 equal size trapazoids around the perimeter.

 

The short side of the trapazoid (up against the pool) will be 56". The diameter at the outer edge of the pool (or the short side of the trapazoid) is 25' 4".

 

The diameter of the long side of the trapazoid  (the outer circumference of the deck) 40' 4".

 

What is the length of the long side of the trapazoid?

 

Thanks in advance for any assistance. 

Answer 1

1) draw an inverted isosceles triangle.

2) Label the bottom vertex "O." This is the center of the pool

3) Label the upper right vertex A and the upper left vertex B. This is one side segment of the pool.

4) Label OA 150", the diameter of the pool

5) Extend OA a little to C, Extend OB to D. CD is the inner side of the trapezoid.

6) Label CD 56" (as given)

7) Extend OAC to E, extend OBD to F. Draw EF, this is the outside of the trapezoid.

8) Label OF 242", this is diameter of outside of trapezoid

9) By similar triangles, EF/DC = OF/OC

10) EF/56 = 242/152

11) EF = 89.16" Now that is longer than the boards you have.