What is the center of mass pentagon w/ missing triangle centered on zero
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What is the center of mass pentagon w/ missing triangle centered on zero

[From: ] [author: ] [Date: 12-04-17] [Hit: ]
The missing piece is one of the five triangles that are formed by drawing lines from the verticies to the center.Area of entire pentagon K = 1.Area of 1 triangle k = .Y value of CM of bottom triangle y = -.Substituting from above,Y cm = +0.......
Object is a regular pentagon(5 equal sides) with a missing triangular piece. Call the length of a side a. The missing piece is one of the five triangles that are formed by drawing lines from the verticies to the center.

-
A little trig will show that:
Area of entire pentagon K = 1.72048*a²
Area of 1 triangle k = .3441*a²
Y value of CM of bottom triangle y = -.4588*a

Ycm = ΣM/ΣA = [K*0 - k*y]/[K - k]
Substituting from above,

Y cm = +0.1147*a
1
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