Mathematics Question and Solution
Radius of the circle, r is;
r² = (8+(3/2))²+4²
r² = (19/2)²+16
r² = ¼(425)
r = ½(5√(17)) cm
Therefore;
Area shaded, exactly in cm² decimal is;
Area sector with radius ½(5√(17)) cm and angle (180-atan(8/19)-atan(16/13))° - Area triangle with height 8 cm and base 6.5 cm - Area triangle with height 8 cm and base 3.36842105263 cm -Area trapezoid with two parallel side 7.36842105263 cm and 8 cm, and height 1.5 cm
= ((180-atan(8/19)-atan(16/13))*π(2.5√(17))²÷360) - (0.5*8*6.5) - (0.5*3.36842105263*8) - (0.5*1.5(7.36842105263+8))
= 98.5251169124 - 26 - 13.4736842105 - 11.5263157895
= 47.5251169124 cm²
