Sir Mike Ambrose is the author of the question.
Calculating Area Purple.
Let the side length of the square be x.
Calculating x.
2(one-sixth x²) = Area Orange
2(1/6)x² = 96
x² = 288
x = 1...
(0.5*(8+3)(8+4)sina)-(0.5*3*8sina) = 36
Calculating angle a.
66sina-12sina = 36
11sina-2sina = 6
9sina = 6
sina = 2/3
a = asin(2/3)
a = 41.8103148958°
Therefore, the required area is;...
Let the side length of the ascribed regular pentagon be 2 units.
a = ⅕*180(5-2)
a = 108°
a is the single interior angle of the ascribed regular pentagon.
b² = 2²+1²-2*1*2cos108
b = 2.49721...
R is;
R² = 2(R-2)²
R² = 2(R²-4R+4)
R² = 2R²-8R+8
R²-8R+8 = 0
(R-4)² = -8+16
(R-4)² = 8
R = 4±2√(2)
Therefore;
R ≠ 4-2√(2) cm.
R = 4+2√(2) cm.
a² = 11*11+10*10-2*11*10cos50
a = 8.92113926968 cm.
(8.92113926968/sin50) = (10/sinb)
b = 59.16920318624°
c = 180-50-59.16920318624
c = 70.83079681376°
d = 0.5a
d = 4.46056963484 cm....
Calculating the area of the ascribed right-angled triangle.
a = (y+2) units.
a is the adjacent base of the right-angled triangle.
b = (z+2) units.
b is the adjacent height of the right-angle...
Radius of the quarter circle is (2+3) = 5 units.
Let a be the side length of the inscribed square.
b²+3² = a²
b = √(a²-9) units.
c = 3+b
c = (3+√(a²-9)) units.
Calculating a.
(3+√(...
tana = 3/4
a = atan(3/4)
b² = 3²+4²
b = 5 units.
cos(atan(3/4)) = 1/c
c = 1.25 units.
c = (5/4) units.
sin(atan(3/4)) = 1/d
d = 1.6666666667 units.
d = (5/3) units.
e = b-c-d
e =...
Calculating angle x.
Let BC be 2 units.
a = 180-70-40
a = 70°
a is angle ACB.
cos70 = 1/b
b = 2.9238044002 units.
b is AB.
c = 180-80-50
c = 50°
c is angle ADC.
d = ½(b)
d = 1...
Sir Mike Ambrose is the author of the question.
Let the side length of the regular hexagon be 1 unit.
Therefore;
Area green is;
Area regular hexagon with side 1 unit + Area regular pentag...
