Calculating Red Area.
Let AB = CD = x.
Let AD = BC = y.
½*xa = 10
a = 20/x units.
a is BQ.
½*xb = 6
b = 12/x units.
b is the horizontal height of area 6 (area triangle APB).
c = y-b
c = y-(12/x...
Calculating area ABCD.
Let x be the radius of the inscribed circle.
a = ½(16)
a = 8 units.
x² = 8²+a²
a = √(x²-64) units.
b = ½(25) units.
It implies;
x ~ 8
½(25) ~ x
Cross Multiply.
x² = 10...
Calculating Area Yellow.
½*a²sin60 = 24
√(3)a² = 24*4
a² = 96/√(3)
a = √(96/√(3))
a = 7.44483887282 units.
a is the radius of the circle.
b = a-x
b = (7.44483887282-x) units.
Calcul...
Sir Mike Ambrose is the author of the question.
Let the single side length of the square be 2 units.
Area square is;
2² = 4 square units.
Calculating green area.
It will be;
Area square of side...
Let the single side length of the ascribed square be 2 units.
Calculating yellow area .
It is;
Area sector with radius 2 units and angle (90-2tan–¹(½))°).
= (90-2tan–¹(½))x4π÷360
= 1.287...
Calculating Area Red.
a = (1+x) units.
a is the diameter of the circle.
b = ½(a)
b = ½(1+x) units.
b is the radius of the circle.
c = ½(1-x) units.
Calculating x.
(½(1+x))² = 2(½(1-x))²
¼(1+2x+...
Calculating x.
Let r be the radius of the inscribed green circle.
Let R be the radius of the ascribed quarter circle.
(R-r)² = r²+5² --- (1).
(R-r)²+5² = a² --- (2).
a² = x²+r² --- (3...
Calculating the area of the ascribed regular octagon.
Let the equal longest length of the both inscribed yellow triangles be x.
a = ⅛*180(8-2))
a = ⅛(180*6)
a = ½(45*6)
a = 135°
a is the single in...
Calculating Length AB.
Let AB = (a+7+b) units.
Calculating a and b.
c = (7+b) units.
Therefore;
a(7+b) = 60
a = 60/(7+b) --- (1).
Again.
d = (a+7) units.
Therefore;
b(a+...
Shaded Area is;
Area circle with radius 4 cm - 4(area quarter circle with radius 4 cm - area isosceles right-angled triangle with equal adjacent lengths 4 cm).
= π*4²-4(¼(4²π)-½(4²))
= 16π-4(4π-8...
