Let the height of the yellow area trapezoid be a.
Calculating a.
tan72 = a/b
b = (a/tan72) cm.
c = 2b
c = (2a/tan72) cm.
d = 8+c
d = (8+(2a/tan72)) cm.
It implies;
½*a(8+(8+(2a/tan72))) = 56....
Considering similar triangles ADC and CDB ratios.
Let CD be a.
16 = a
a = 4
Cross Multiply.
a² = 64
a = 8 units
c² = 16²+8²
c = 8√(5) units.
c = AC.
Calculating r1.
16r1+8r1+8√(5)r1 = (16*8)...
Calculating a.
(1/sin120) = (a/sin20)
a = 0.39493084363 units.
Calculating b.
(1/sin120) = (b/sin40)
b = 0.74222719897 units.
Therefore, observing the proof;
(1/a)+(1/b) = 3ab+3
(1/a)+(1/b) is...
Notice;
a² = 5² - (⅕(√(481)))²
a = ⅕(12) units.
b = 5-a
b = ⅕(13) units.
c² = 4²-(⅕(12))²
c = ⅕(16) units.
d = atan(4/3)°
(a) Area A exactly is;
½*⅕(16)*(5+⅕(13)) - atan(4/3)π*16/360
= ((8*38...
Let AB be 1 unit.
BC = 3 units.
It implies;
AC = 1+3
AC = 4 units.
AC is a side length of the square.
Radius of the inscribed half circle a is;
½(BC)
a = ½(3) units.
a = 1.5 units.
b = 1.5+AB
b...
Let a be 1 unit.
(1/sin48) = (b/sin24)
b = 0.54731813925 units.
(1/sin48) = (c/sin108)
c = 1.27977277603 units.
DC = 1.27977277603+0.54731813925+1
DC = 2.82709091528 units.
Therefore, the requi...
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Let the small inscribed circle's radius be x.
x = 6 cm.
Let the big inscribed circle's radius be y.
y = 8 cm.
Let the ascribed semi circle's radius be z.
= 18 cm.
a² = 10²-8²
a = 6 cm.
b² = 12²...
Let r be the radius of the circle.
3x+3 = 2r --- (1).
r² = (r-1)²+(r-2x)²
r² = r²-2r+1+r²-4xr+4x²
4xr+2r = r²+4x²+1 --- (2).
From (1).
3x+3 = 2r
x = ⅓(2r-3) --- (3).
Calculating r.
Therefore,...
Notice;
Hexagon Area = 24√(3) square units.
Calculating hexagon side length.
Let it be a.
(6a²)/(4tan30) = 24√(3)
½(3√(3))a² = 24√(3)
3a² = 48
a = 4 units.
Equation of the curve is;
y = ½(x²)...
