Sir Mike Ambrose is the author of the question.
Area red exactly as a single fraction is;
Area triangle red with two lengths ⅓(24-8√(3)) cm and ⅓(18-8√(3)) cm, and angle 60°
= ½(⅓(24-8√(3)))...
Please, move the above question left/right one time to review the solution.
Thank you.
Area Square OBCD is;
½(3+2√(2)) square units.
Let a be the radius of the inscribed circle.
b = a+2a
b = 3a units.
c² = 2(3a)²
c = 3√(2)a units.
d = 180-45
d = 135°
Calculating a.
5² = (3√(2)a)²+a²-2*3√(2)a²cos135
25 = 19a²+6...
Calculating L.
Let a be the width of the rectangle.
b = (a-x) units.
a(a-x) = 4 --- (1).
Observing similar plane shape (right-angled) side length ratios.
(a-x) - ½(L)
L - a
Cross...
½(a*a) = 10
a² = 20
a = 2√(5) units.
a is the equal adjacent lengths of the inscribed purple isosceles right-angled triangle.
Let c be the side length of the square.
tand = c/(0.5c)
d = a...
Notice.
3x = 15
It implies;
x = 5 m.
x is the width of the inscribed green rectangle.
The length is 15 m.
Therefore, area inscribed green rectangle is
5 *15
= 75 m²
Let the square side be a.
a² = πr²
And r = 1 unit, π = 22/7
a² = (22/7)
a = √(22/7) units.
b = ½(a)
b = ½√(22/7) units.
c² = 2a²
c² = 2√(22/7)²
c = √(44/7)
c = ⅐(2√(77)) units.
c...
Calculating MN, diameter of the yellow semi circle.
Let the radius of the yellow semi circle be a.
b = ½(3+3+2)
b = 4 units.
b is the radius of the bigger semi circle.
c = b-3
c = 1 uni...
sin30 = 1/a
½ = 1/a
a = 2 units.
cos30 = ½(a)/b
½√(3) = 1/b
√(3)b = 2
b = ⅓(2√(3))
b = ⅓(2√(3)) units.
b = 1.1547005384 units.
b is the radius of the ascribed semi circle.
Calculating...
Let CN = a
b = (9+a) m.
b is the side length of the square.
c = ½(b)
c = ½(9+a) m.
c = CM = DM.
Calculating a.
(9+a) - ½(9+a)
½(9+a) - a
Cross Multiply.
a(9+a) = ¼(9+a)²
a =...
