Red Area is;
7(area square with side 1 unit) - Area triangle with base 1 unit and height 4 units - Area square with side 1 unit - Area triangle with height and base 1 unit respectively.
= 7(1*1) -...
Let the radius of the inscribed yellow half circle be x.
Calculating x.
a = tan(3/4)°
a is angle ABC.
b = tan(4/3)°
b is angle BAC.
sin(atan(3/4)) = x/c
c = (5x/3)
c is OB.
sin(a...
Let the inscribed blue square side length be x.
It implies;
Considering side lengths of similar right-angled triangle.
2 - x
x - 6
Therefore;
(2/x) = (x/6)
Cross Multiply.
x² = 12
Area Blue = 1...
Let the side of the green square be x.
Therefore;
x/(tan(atan¾)) + x + x/(tan(atan(4/3))) = 5
⅓(4x) + x + ¼(3x) = 5
16x + 12x + 9x = 60
37x = 60
x = (60/37) units
It implies;
Area squ...
Let the three equal lengths be 1 unit.
it implies;
AB = BD = DE = 1 unit.
a² = 1²+1²-2*1*1cos100
a = 1.5320888862 units
a is AD.
c = ½(180-100)
c = 40°
c is angle ADB.
d = 180-40-40...
r, radius of the quarter circle is;
r = 8+6
r = 14 units.
a = 180-60
a = 120°
It implies;
Calculating x, observing Cosine Rule.
14² = 6²+x²-2*6*xcos120
196 = 36+x²+6x
x²+6x-160 = 0...
Sir Mike Ambrose is the author of the question.
y = 2^(x)
P coordinate is;
P(1, 2)
dy/dx = 2^(x)In2
For x = 1
dy/dx = 2In2
It implies;
Q coordinate is;
Q(0, (2-2In2))
Therefore;...
Calculating x.
a =4x-x
a = 3x
tanb = 3x/4x
b = atan(3/4)°
c = atan(4/3)°
d = ½(c)
d = 0.5atan(4/3)°
It implies
tan(0.5atan(4/3)) = 4/e
e = 4/(tan(0.5atan(4/3)))
e = 4/(0.5)
e = 8 units.
It...
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Let the three equal lengths be a.
Radius r of the semi circle is;
r = 5+4
r = 9 units.
5² = b²+a²-2abcos45
25 = b²+a²-√(2)ab --- (1).
9² = b²+a²-2abcos135
81 = b²+a²+√(2)ab --- (2).
Solving (1)...
