Mathematics Question and Solution
Let the small inscribed half circle be r.
Big inscribed half circle's radius is 0.5 cm.
Calculating r.
(0.5+r)² = 0.5²+(1-r)²
0.25+r+r² = 0.25+1-2r+r²
3r = 1
r = ⅓ cm.
1² = 2a²
a = 1/√(2)
a = 0.70710678119 cm.
b = 0.70710678119-(1/3)
b = 0.37377344785 cm.
b is the height of triangle ABC.
c = 0.5-(1/3)
c = (1/6) cm.
d² = (1/2)²-(1/6)²
d = ⅓√(2) cm.
d = 0.47140452079 cm.
e = 2(0.70710678119-0.47140452079)
e = 0.4714045208 cm.
e is the base of triangle ABC.
It implies;
Area Triangle ABC is;
0.5*0.4714045208*0.37377344785
= 0.08809924654 cm²
