Mathematics Question and Solution
(4+5+3)² = 2a²
a² = 72
a = 6√(2) cm.
a is the congruent adjacent sides of the right-angled triangle.
b² = √(72)²+3²-2*√(72)*3cos45
b² = 81-36
b = √(45)
b = 3√(5) cm.
(3√(5)/sin45) = (3/sinc)
c = 18.4349488229°
d² = √(72)²+4²-2*√(72)*4cos45
d² = 88-48
d = √(40)
d = 2√(10) cm.
(2√(10)/sin45) = (4/sine)
e = 26.5650511771°
f = 90-c-e
f = 90-18.4349488229-26.5650511771
f = 45°
2g² = 5²
g² = 25/2
g = √(25/2)
g = ½(5√(2)) cm.
g = 3.5355339059 cm.
It implies;
Shaded Area is;
Area quarter circle with radius ½(5√(2)) cm - Area isosceles right-angled triangle with adjacent sides ½(5√(2)) cm each.
= ¼*π(½(5√(2)))²-½(½(5√(2)))²
= ((50)π)/16 - ⅛(50)
= ⅛(25π)-⅛(50)
= ⅛(25π-50)
= 25(π-2)/8 cm²
= 3.5674770425 cm²
