Hi there! Thank you for the opportunity to help you with your question!
First, the centroid of a composite shape is equal to the weighted average of the centroid of the simple shapes. The centroid of a square (left part of the figure), is the midpoint position (5,5).
Now we look at the triangle, which has base= 8 and height = 10. The centroid of a right triangle is (b/3,h/3) if the triangle's right-angle vertex is at the origin. Since the vertex is at (10,0), the centroid is:
Now we need to take the weighted average:
x_centroid = (38/3*40 + 5*100)/140 = 7.19 [this formula is centroid_triangle*area_triangle + centroid_square*area_square, all divided by total area
y_centroid = (10/3*40 + 5*100)/140 = 4.52
So the centroid is at (7.19, 4.52) inches
Please let me know if you need any clarification. Always glad to help!
Sep 1st, 2015
Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.