No, no... I didn't use your numbers.
Post #5 is mine too;
In my post #6, I wrote that "it may work" because I knew that that would work!
CD can be any number; it doesn't have to be 2.
I had to give the dimension to CD in order to find out the ratio between the yellow area and the area of the rest of the sector (I named it a double-segment area)
CD is a radius of a circle.
After that, it was easy, using the proportion, to calculate the area of the double-segment when the yellow area is 1 square unit.
I'm very bad at explaining things...
This actually may work:
1/ We may find the ratio of the area of the double-segment to the yellow area. (That ratio doesn't change with the circle size)
2/ We can use that ratio and calculate the double-segment area.
3/ If CD = 2 then Yellow area = 1.369706513
4/ If CD = 2 then Double-segment area = 0.724688589
1.369706513 : 0.724688589 = 1 : x
x = 0.529083115
Area of a sector = 1 + x = 1.529083115
Area of a circle = 6(1 + x) = 9.17449869
AB = 2[sqrt(9.17449869 / pi)] = 3.417796737
This is very hard to explain. I don't blame you if you do not understand it...
I checked these numbers, and it works.
WYZ is equilateral and WXY is isosceles with a vertex angle of XWY. If the perimeter of the entire figure is 22 units and the area of the entire figure is 15√3, what are the sides lengths of each side of each triangle?
I find this question very interesting, and here's my answer: