Area green is;
Area triangle with height 8 unit and base 8√(3) unit - Area sector with radius 8 unit and angle 30° + Area sector with radius 8 unit and angle 60° - 2(area triangle with height 8 uni...
Let r be the radius of the circle.
Calculating r.
12² = r²+a²
a² = 144-r²
a = √(144-r²).
tanb = r/a
tanb = r/√(144-r²) --- (1).
tanb = a/3r
tanb = √(144-r²)/(3r) --- (2).
Equating (1) and (2)....
Area blue total, exactly in cm² decimal is;
Area trapezoid with parallel sides (80/7) cm and ((80/7)+21.4285714284) cm, and height 20 cm - Area trapezoid with parallel sides 20 cm and ((80/7)+12.24...
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Side length of the square is;
Let it be x.
x = √((16*34)-144)
x = √(400)
x = 20 cm.
Therefore;
Area Orange exactly in decimal cm² is;
Half area square with side 20 cm - Area triangle with height...
4^(2x)+2 = 3*4^(x)
Let 4^(x) = p
It implies;
p²+2 = 3p
p²-3p+2 = 0
Resolving the above quadratic equation.
p²-p-2p+2 = 0
p(p-1)-2(p-1) = 0
(p-2)(p-1) = 0
Therefore;
p = 1 or p = 2
And p = 4^(x...
Let the blue square side length be x.
2² = a²+b²
b² = 4-a²
b = √(4-a²)
4² = a²+(√(4-a²)+x)²
16 = a²+((4-a²)+2x√(4-a²)+x²
12 = 2x√(4-a²)+x² --- (1).
5² = (x+a)²+(4-a²)
25 = x²+2xa+a²+4-a²
21 = x²+...
a = ½(8+2)
a = 5 cm.
a is the radius of the ascribed semi circle.
b = 8
2 = b. Cross Multiply.
b² = 16
b = 4 cm.
Therefore, area Blue is;
½(8*4)
= ½(32)
= 16 cm²
Calculating Area Red.
tanc = 4/3...
Sir Mike Ambrose is the author of the question.
Let the side of the regular pentagon be 1 unit.
a = 360-2(108)-90
a = 54°
tan72 = b/0.5
b = 1.53884176859 units.
tan54 = 1.53884176859/c
c = 1.1180...
Notice.
a = 18+55 = 73°
b = 28+45 = 73°
It implies;
The ascribed triangle is isosceles.
Calculating angle x.
Let the shorter length of the ascribed isosceles triangle be 1 unit.
c = 180-45-55-1...
