Question

6. Locate the centroid (TT) of the shaded area. Ans: (2,5) = (-1.18, 1.39 m 1m 3m - 3 m +3m-

Please show all working. Thanks

Answer 1

it Region: Triangle Area of triangle a zx base x height 12 x 3x3 A = 4.5 m² 5-(/3+ 3) --(m + 3) - Lion-4 I 2 4 3 = lm and Region: Rectangle Area of Rectangle a base x height a 3x3 A2 = 9 m² ă, 2-b% 2-1.5m Yoh 1.5m

3rd resion Area of Quatter Cirullar area (rolm) this resion -Tr% A = 0.7854 m² Kg = Lene por = -0.4244m Y = 48 2 0.4244m 4th Region Quarter- Greular area (821m) Area of this region & Tr/ A = 0.7854 m 2 0.4244m Y = her - 0.4244m 5th Resion quasher Creular area (823m) Area of this resion of A5 27.0685 m2 Rosar 1.2732 m Yshop 1.2982 m

Now, the centrsid of shaded area x x x, -, - 4, А,Х, Alto - Ag-Aut A5 [4.5*(-4)] + [gx (-1.5)] – [0.7854x (-0.4244)] -[07854x604244)]+[7.06854 C1-2932)] 4.5+9 -0.7854-0.7854 +7.0685 9 Je a-18-13.5+ 0.3333 -0.3333 + /14661 [ 2 -1.1842 m. A. Y = AX + A2 Y2 - A3Z - A4 94 + As Y5 Alt A2 A3 - Antas + [4-5x60] + [9x C1:50] -10.7854x (0-4246)] - (0.7854x C0-4244)] + [4.0685% (1.2732)] 4.5+9 -0.7854 -0.7854 +7.0885 = 4.5+ 13.5 - 83333 -0.3333 + 9 [9 21.3859 m Am