Mathematics Question you amazingly
Calculating A+B Area.
a = 2*3√(2)
a = 6√(2) units.
a is the diagonal of the square.
2b² = 2a²
2b² = (6√(2))²
2b² = 2*36
b = √(36)
b = 6 units.
b is the side length of the square.
Calculating Area A.
Area A is;
¼(π(0.5*6)²)-(45π*(3√(2))²/360)+(½*3*3)
= ¼(9π)-⅛(18π)+½(9)
= ⅛(18π-18π+36)
= 9/2 square units.
Calculating Area B.
c = (6-3√(2)) units.
Area B is;
½(6*6)-(45π*(3√(2))²/360)-(¼*π*(6-3√(2))²)
= 18-⅛(18π)-(¼*π*(54-36√(2))
= 18-⅛(18π)-¼(54π)+¼(36√(2)π)
= ⅛(144-18π-108π+72√(2)π)
= ¼(72-63π+36√(2)π)
square units.
Therefore, A+B Area is;
(9/2)+¼(72-63π+36√(2)π)
= ½(9)+¼(72-63π+36√(2)π)
= ¼(18+72-63π+36√(2)π)
= ¼(90-63π+36√(2)π) square units.
= 13.0058621494 square units.
= 13 square units.
