EG = 3AG
Let AG = 1 unit.
Therefore;
EG = 3 units.
The side length of the regular pentagon is;
AG+EG = 1+3 = 4 units.
AE = 4 units.
It implies, Area Blue is;
0.5*2*4sin108
= 4sin108
= 3.80422606...
Sir Mike Ambrose is the author of the question.
Let the side of the blue square (length CD) be 1 unit.
Area Blue is;
1²
= 1 square unit.
a = 180-20-40
a = 120°
(b/sin40) = (1/sin20)
b = 1.87938524...
Let the side length of the regular pentagon be 2 units.
(CF)² = 5-4cos108
CF = 2.49721204096 units.
CF is the side length of the blue regular triangle and radius of the sector CGF.
Area Blue is;...
Let AO be 1 unit.
AB will be 2 units.
Therefore, radius r of the ascribed semi circle is;
= 3 units.
Area semi circle is;
½(3²)π
= ½(9π) square units.
tana = (1/3)
a = atan(⅓)°
b = (180-2atan(½...
Sir Mike Ambrose is the author of the question.
Let the side of the inscribed square be a.
Calculating a.
¾ = a/b
b = ⅓(4a)
It implies;
½*a*((⅓(4a))+3a) = 78
⅙(13a²) = 78
⅙(a²) = 6
a = 6 cm.
b =...
Calculating x.
Let the two congruent lengths of the plane shape be 1 unit.
(a/sin11) = (1/sin22)
a = 0.50935834748 units.
(b/sin147) = (1/sin22)
b = 1.45389601942 units.
c = 1+a
c = 1.5093583474...
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Sir Mike Ambrose is the author of the question.
⅓(4) = a/9
a = 12 cm.
let alpha be b.
Calculating b.
(2tanb/(1-tan²b)) = (4/3)
2tan²b+3tanb-2= 0
b = atan(½)°
½ = c/9
c = 4.5 cm.
d...
Notice;
AB = AC
(6.84/sin40) = (a/sin70)
a = 9.99941104856
a = 10 cm.
a is AB = AC.
(9.99941104856/sin155) = (b/sin15)
b = 6.12381965823 cm.
(9.99941104856/sin155) = (c/sin10)
c = 4.10862393682...
