Mathematics Question and Solution
Let the side length of the three equal regular triangles be 2a units each.
b² = 2a²-2a²cos120
b = √(3)a unit.
(6√(7))² = (2a)²+(√(3)a)²-2*2a*√(3)acos90
252 = 4a²+3a²
252 = 7a²
a² = 36
a = 6 units.
It implies;
2a
= 2*6
= 12 units.
Where 12 units is the side length of the three equal regular triangles each.
b = √(3)a
And a = 6 units.
b = 6√(3) units.
Therefore, paint area is;
3(area triangle with height 6√(3) units and base 12 units + area triangle with height 6 units and base 6sin120 units).
= 3((0.5*6√(3)*12)+(0.5*6*6sin120))
= 3(36√(3)+9√(3))
= 3(45√(3))
= 135√(3) square units.
