Equal trapazoids around the circumference of a circle

Waterlogged

New member
Joined
May 19, 2018
Messages
1
'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
 
'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
What is the outer circumference of the deck? = Pi * (484)

Divide that into 17 equal parts. What do you get?
 
'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?

Think of similar triangles.

If you extend the legs of a trapezoid until they meet at the center, you will have two similar isosceles triangles. The inner one has legs (assuming you measured the diameter of the circle on which the ends of the straight rails lie, that is, the diameter of the circle in which the 17-gon is inscribed) of (25' 4")/2 = 12' 8", and base 55". (I'm using the pool rails here rather than the inner edge of the deck, 56", because I assume that is where the diameter is measured. But that may depend on how the measurements are made.) The outer trapezoid has legs (40' 4")/2 = 20' 2". This gives a proportion,

x : 20' 2" = 55" : 12' 8".

Can you solve that?

If you need further help, I'll first want to be sure I'm interpreting the situation correctly. Can you confirm how you are measuring the 25' 4" "diameter" of a pool that is not really a circle? What points are that far apart? The fact that there are an odd number of sides makes this a little tricky, I would think. The fact that rails have a non-zero thickness may also complicate it -- are you measuring inside or outside or center of the rails?

Khan's answer seems to assume that you have arcs, not straight sides.
 
Top