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Google Chrome https://session.masteringengineering com/myct/itemview?assignmentproblemi Dn 5371392 EM2413-Statics-Hibbeler Hww10 Problem 9.65 previous l 9 of 0 l return to assignment Problem 9.65 Part A Suppose that La 2.1 in. (Egure 1) Determine the location (a, y) of the centroid Cof the area Express your answers using three significant figures separated by a comma. Submit My Answers Give up Figure 1 of 1 Provide Eeedback C

Solution

area of square of length 2L = 4L^2

area of quadrant = /4 * L^2

area of right isosceles triangle =1/2 L^2

centroid of square= (L,L)

centroid od quadrant= (4L/3 ,4L/3)

centroid of right triangle = (5L/3,5L/3)

coordiantes of right triangle = (L,2L),(2L,L),(2L,2L)

so centroid = ((L+2L+2L)/3,(2L+L+2L)/3)

= (5L/3,5L/3)

now given area is obtaine by removing quadrant and right triangle from square

hence x-cordinate of centroid of given figure is

(4L^2(L) - /4 * L^2*(4L/3) - 1/2L^2 *( 5L/3))/(4L^2- /4 * L^2 - 1/2L^2 )

= L(4-1/3 - 5/6)/(4-/4 -1/2)

=L*1.04373

=2.1*1.04373

= 2.19184

since it is symmentric about y= x ,

y-coordinate of centroid is also 2.19184

hence (2.19184,2.19184)