Sir Mike Ambrose is the author of the question.
Area largest square is;
(3√(5))²
= 45 cm²
Area purple is;
Area triangle with height equal base equal 3√(5) cm - area triangle with side 2....
Let AB = CD = 1 unit.
a = 180-40-30
a = 110°
a is angle CAD.
(1/sin110) = (b/sin40)
b = 0.6840402867 units.
b is AC.
Therefore, the required angle, x is;
(0.6840402867/sinx) = (1/si...
Calculating area shaded blue.
a² = (2+√(3))²+(3+2√(3))²
a² = 4+4√(3)+3+9+12√(3)+12
a² = 28+16√(3)
a = √(28+16√(3)) units.
a = 7.4641016151 units.
a is the hypotenuse of the ascribed right-a...
Let the side length of the regular octagon be 1 unit.
a = ⅛*180(8-2)
a = ⅛(180*6)
a = 135°
a is the single interior angle of the regular octagon.
2b² = 1²
b² = ½
b = ½√(2) units.
c =...
Let the side length of the inscribed regular hexagon which is equal the side length of the ascribed regular nonagon be 1 unit.
a = ⅙*180(6-2)
a = 120°
a is the single interior angle of the ins...
a = 180-45-75
a = 60°
b = 180-75-60
b = 45°
c = a-b
c = 15°
d = 180-60-45-c
d = 60°
e = 180-45-d
e = 75°
Therefore, the required angle, alpha, let it be f, is;
f = 180-d-e
f...
a = 1+1.5
a = 2.5 units.
b²+1.5² = 2.5²
b² = 6.25-2.25
b = √(4)
b = 2 units.
Let c be the radius of the ascribed semi circle.
d = 1+2
d = 3 units.
e = (3-c) units.
f = 1.5+e
f =...
Let the base of the inscribed green triangle be a.
b = (8-a) units.
c² = a²+8²
c = √(a²+64) units.
It implies;
(8-a)+8 = √(a²+64)
(16-a)² = a²+64
256-32a+a² = a²+64
32a = 192
4a =...
Area Orange exactly in fraction is;
Area triangle with height. 7.87908624144 units and base 4.37727013143 units + Area triangle with side (38/9) units and 9.01335086564 units, and angle 53.01709...
Let MP be 2 units.
a² = 1²+1²
a = √(2) units.
2b² = 1²
b² = ½
b = ½√(2) units.
c = a+b
c = ½(3√(2)) units.
d² = 1²+(½√(2))²-2*1*½√(2)cos135
d = 1.5811388301 units.
Therefore, th...
