a = 4+8
a = 12 cm.
a is the radius of the quarter circle.
tanb = 12/4
b = atan(3)°
c = (60+atan(3))°
(12/sin(60+atan(3))) = (4/sind)
d = 14.4420678686°
e = 180-60-atan(3)-d
e = 12...
b = 8-a
It implies;
27^(a)/3^(8-a) = 81
3^(3a) = 3^(8-a)*3⁴
3a = 8-a+4
3a = 12-a
4a = 12
a = 3.
Calculating b.
b = 8-a
And a = 3
b = 8-3
b = 5
Let the square side be x.
Calculating x.
a = (5-½(x)) units.
b = (5-x) units.
It implies;
5² = (5-½(x))²+(5-x)²
25 = 25-5x+¼(x)²+25-10x+x²
¼(5x²)-15x+25 = 0
¼(x²)-3x+5 = 0
x²-12x+20 = 0
Resolvi...
The side of area green, inscribed square is;
Let it be x.
Therefore;
1.11496246101x + 0.82101781219x = 27.3672604063
1.9359802732x = 27.3672604063
x = 14.1361256544 cm
Therefore;
Exact perimeter...
Let BC be 1 unit.
a = 180-18-64
a = 180-82
a = 98°
a is angle BDC
(1/sin98) = (b/sin18)
b = 0.3120538813 units.
b is BD
c = 180-4-18-64-46
c = 180-132
c = 48°
c is angle BAC.
(1/sin48) = (d/sin2...
Let AC be 1 unit.
Area smaller pentagon is;
½(5)*(1/(2tan(36)))
= 1.72047740059 square units.
a² = 1²+0.5²-cos108
a = 1.24860602048 units.
Where a is CD.
(1.24860602048/sin108) = (0.5/sinb)
b = 2...
Area Blue is;
Area trapezium with two parallel side 4 cm and 1 cm, and height 4 cm - Area semi circle with radius 2 cm.
= ½*4(4+1) - ½(4π)
= 10 - 2π
= 2(5-π) cm²
a = 180-12-2-46-8
a = 180-68
a = 112°
a is angle ABC.
Let AC be 1 unit.
It implies;
(1/sin112) = (b/sin14)
b = 0.257447904 units.
b is AB.
c = 180-8-2
c = 170°
c is angle ADC.
It implies;
(1/sin...
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tana = 12/8
a = atan(3/2)°
b = 180-a
b = (180-atan(3/2))°
(10/sin(180-atan(3/2))) = (4/sinc)
c = 19.4400348282°
d = 180-b-c
d = 180-19.4400348282-(180-atan(3/2))
d = 36.8698976458°
e = 90-d
e =...
