jugoslav

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...

In geometry, there's always more than one way to solve a problem. Although our answers are the same, your method 

is more mathematical than mine. Good job. Melody! 

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

PROPORTION:

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. 

The original question was not correct (Link:https://web2.0calc.com/questions/geometry_81360) so I repost it here.

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? 

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I find this question very interesting, and here's my answer:

median * height = area

median = 60 / 8

First triangle:

A = a²(√3 / 4) 

Second triangle: 

Side = 4 / cos15º

Area = a²(√3 / 4)

The rest of this problem is entirely up to you. Good luck! 

I gave you a plus for your concept. Kudos! 

There is a circle in the coordinate plane. If the radius doubles, the area increases by 10 units. Find the new radius of the circle.

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Radius => r             New radius => 2r

A = r²pi                    A_n = (2r)²pi             (A_n = A + 10)

A_n - A = 10

(2r)²pi - r²pi = 10

Try to use this formula:

(Shorter leg => a         Longer leg => b           Hypotenuse => c)

This is very simple. 

ΔABE ~ ΔCDE

BE = x         CE = y

x/18 = y/12

12x = 18y

y = 12x / 18

18 / 21-y = 12 / 19-x

18(19-x) = 12(21-y)

18(19-x) = 12(21- 12x/18)

x = 9         y = 6

I'll let you finish up your homework. 

Shaded area = 7.85398163 square units

or

A = 2.5pi     = 5pi/2

Find the smallest value of x such that x^2 + 10x + 25 = 4.

x² + 10x + 21 = 0

x = -3,     x = -7

Equilateral triangle area       A = √3

Circle radius       r = 2/3(√3)

Circle diameter   z = 2r

Height       h = A / z

(w² + h²)+(h² + (z-w)²) = z²

x = sqrt(w² + h²)

y = sqrt(h² + (z-w)²)