Calculating Area Shaded.
Let r be the radius of the semi circle.
Calculating r.
((6r/√(10))-2)²=(r/2)²+(3r/2)²
72r²-48√(10)r+80=50r²
22r²-48√(10)r+80= 0
11r²-2⁴√(10)r+40= 0
Therefore...
Calculating area of the inscribed red square.
Let a be the side length of the inscribed red square.
2b² = a²
b = √(a²/2)
b = ½√(2)a units.
10² = a²+(½√(2)a)²-2a*½√(2)acos(45+90)
100 = ½...
Let the base of the quadrilateral be 1 unit.
a = 180-58-28-38
a = 180-124
a = 56°
(1/sin56) = (b/sin(58+28))
b = 1.2032796622 units.
(1/sin56) = (c/sin38)
c = 0.7426219217 units.
d...
Let the ascribed quarter circle radius be 1 unit.
2a² = 1²
a² = ½
a = ½√(2) units.
a = 0.7071067812 units.
a is the radius of the blue inscribed quarter circle.
Area blue inscribed quarte...
Sir Mike Ambrose is the author of the question.
Let the single side length of the small square be 1 unit.
Therefore;
Area large square is;
((1/tan15)-1)²
= 7.46410161514 square units....
Sir Mike Ambrose is the author of the question.
The width of the rectangle is;
(5/2)+(11/2)
= 8 cm
Area Rectangle is;
12*8 = 96 cm²
Area Green is;
½(7*12)sin((90-atan(5√(3)/11)))...
Let the square side length be 1 unit.
tan15 = a/1
a = 0.2679491924 units.
b = 1+a
b = 1.2679491924 units.
c = 1-a
c = 0.7320508076 units.
d² = 1²+1²
d = √(2) units.
e = 90-15
e...
Let the length of the two congruent rectangle be 1 units.
Let the width be x.
Therefore;
1 ~ (1+x)
x ~ 1
It implies;
1/x = (x+1)/1
x²+x-1 = 0
(x+½)²=1+¼
x = -½±½√(5)
Therefore...
Let the side length of the blue inscribed equilateral triangle be 1 unit.
Area blue equilateral triangle is,
0.5*1²*sin60
= ¼√(3) square units.
= 0.4330127019 square units.
It implies;...
Sir Mike Ambrose is the author of the question.
The equation of the curve is;
Using the points;
(4, 4), (2, 0), (12, 0)
And, y =ax²+bx+c
Therefore;
4=16a+4b+c
0=4a+2b+c
0=144a+12b...
