Mathematics Question and Solution
a² = 2(1)²
a = √(2) units.
a is the diagonal of the inscribed square and also the side length of the two congruent inside bigger regular triangle.
b = ½(a)
b = ½√(2) units.
c²+b² = a²
c² = √(2)²-(½√(2))²
c² = 2-½
c = √(3/2)
c = ½√(6) units.
c = 1.22474487139 units.
c is the height of the two congruent bigger inscribed regular triangle.
d = c-b
d = ½√(6)-½√(2)
d = ½(√(6)-√(2)) units.
d = 0.51763809021 units.
e = 180-60-45
e = 75°
f = 180-30-75
f = 75°
g² = 2*0.51763809021²-2*0.51763809021²cos30
g = 0.26794919243 units.
Let the side length of the inscribed regular yellow triangle h.
j = ½(1-h) units.
Calculating h.
cos60 = ½(1-h)/0.26794919243
0.13397459622 = 0.5-0.5h
0.5h = 0.5-0.13397459622
h = (0.36602540378)/0.5
h = 0.73205080756 units.
Again, h is the side length of the inscribed yellow regular triangle.
Area inscribed regular yellow triangle is;
0.5*0.73205080756²sin60
= 0.23205080756 square units.
