# Finding the centre of mass of a trapezoid

The figure shows a symmetric trapezoidal plate with a base of '2L'. The height and the top are each of length 'L' and the plate is of uniform density. Find the centre of mass of the trapezoid.

P.S i have not included figure as scanner not working assuming know what it should look like. A rectangle with two triangles stuck on each side with measurements as given.

https://brainmass.com/physics/physics-measurements/finding-centre-mass-trapezoid-7407

#### Solution Preview

See figure..

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<br>We know that the centre of mass lies on the red line, since this is a line of symmetry of the object.

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<br>If we label this line the x-axis and introduce a y-axis as in the figure, this will allow us to use calculus:

<br>divide the shape in to small elements. See figure..

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<br>Each strip is a distance of x from the y-axis. The mass of each strip is its volume Ã ? density. The volume of each ...

#### Solution Summary

Very detail answer with easy to understand steps. It will enable you to do similar problems yourself.