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 =...
Shaded area is;
Area under the curve at points (-1, 0) and (7, 0) - Area triangle with height 4 unit and base 8 unit.
= ⅓(208) - ½(4*8)
= ⅓(160) space unit.
Area S is;
Area under the curve at p...
Let the side of the regular hexagon be 1 unit.
Therefore;
Area blue is;
2(area triangle with height 1 unit and base (⅓√(3)) unit).
= 2(½*1*(⅓√(3)))
= ⅓√(3) space unit.
Area orange is;...
Area blue is:
Area triangle with height 1 cm and base (3sin(109.471220634)) cm.
= 0.5*1*3sin(109.471220634)
= 1.41421356238 cm²
= √(2) cm²
Let the radius of the inscribed white semi circle be r.
Therefore;
r²+(1+r)²=(2+r)²
r²+1+2r+r²=4+4r+r²
r²-2r-3 = 0
(r-1)² = 3+(-1)²
(r-1)² = 4
r = 1±2
r ≠ -1
r = 3 unit.
It implies;
Area blue is;...
