CPhill

22^22 * 11^11  =

[ 2 * 11 ] ^22 * 11^11  =

2^22 *  11^22 * 11^33  =

2^22 *  11^33

2^1 = 2

2^2 = 4

2^3 = 8

2^4 = 16    and repeats in a cycle of four

2^22 will end  in  a 4

11^any positive integer power ends in a 1

So

22^22 * 11^11   ends in  a  4

M = 90  - 10  =  80°

Supplement of M  =   180  - 80  =   100°

x + x = 180°

2x = 180°

x =  180 / 2 =    90°

I only see one shaded region........half of the larger circle

Area =  32 pi

Area of smaller square =  x^2

Area of larger square=  (2x)^2 = 4x^2

Ratio of areas =   x^2 /  4 x^2  =     1  / 4

4 feet  =  48 inches

12 feet = 144 inches

On two oppositie sides of the framing we will have   48 / 2 =  24 tiles on each side

On the other two sides of the framing we will have  144 / 2 =  72 tiles on  each side

Plus.....we have 4 tiles on the  corners

Total cost =  [ 2 * 24 + 2 * 72  +  4 ]   *  .10  =    $19.60

Since  EF ll GH, then arcs  EH and FG are equal  .....so....

 x^2 - 2x =  65 - 3x

x^2 + x - 65   =  0 

x ≈ 7.58

So   arc EH = arc FG =  65 - 3(7.58)  =  42.26°

Then arc EPF  = 

360 - 2 * arc EH  - arc  GH

360  - 2(42.26) - 70   ≈ 205.5° 

Area of square =  (12/4)^2  = 3^2  = 9

Area of equilateral   triangle =   (1/2) * 4^2  * sin (60°) =  8 sqrt (3) / 2  =  4sqrt (3)

Ratio of areas  =   [ 4sqrt (3) ]  / 9

ab + a + b  =

7 * 13  + 7 + 13  =

91 + 20 = 

111

110 less

Circumradius =      product of the sides  / [4 * area ]  =   (5 * 6 * 4.5)  /(4 * 11)  ≈  3.07 cm