023 m 49 028 m 0 14 O 37 m 04 m 0 14 m Answer X SolutionRega

0.23 m 49° 0.28 m 0. 14 O. 37 m 0.4 m 0. 14 m Answer: X=

Solution

Regard each trapezoidal piece as the sum of a 23 cm x 28 cm rectangle and a right triangle whose legs are 23 cm and (23 cm)/tan(49 deg) = 20cm. The x-coordinate of the center of the 23x28 rectangle will be at 40 +(28/2)*cos(49) - (23/2)*sin(49) = 40.5 cm

The x-coordinate of the center of the triangle is tricky. If the angle were 45 degrees, the x-coordinate of the centroid of the triangle would be 40 cm - (23 cm)/sqrt(2) = 23.7 cm. For the moment, I\'m going to use that, and finish the rest of the calculation.

The x-coordinate of the center of the big rectangle plate = 20cm

The area of all the plates combined is 40*65 + 20*23 + 2*23*28 = 2600 cm^2 + 460 cm^2 + 1288 cm^2. The x-coordinate of the centroid of the whole object is:
(20*2600 + 23.7*460 + 40.5*1288) / (2600 + 460 + 1288)
= 26.4cm