Centroids
A centroid is the center of balance, center of gravity, and center of mass.
Finding the centroid
Symmetrical objects
The interception of lines of symmetry determine where a symmetrical shape's centroid is.
Square- To find the centroid of a square, you must find half of the height and half of the base.
Triangle- The centriod of a triangle is at 1/3 of the base and 1/3 of the height.
Semi circle- Use the equation 4(radius)/3(pi) to find the centroid.
Square- To find the centroid of a square, you must find half of the height and half of the base.
Triangle- The centriod of a triangle is at 1/3 of the base and 1/3 of the height.
Semi circle- Use the equation 4(radius)/3(pi) to find the centroid.
Complex shapes
To find the centroid of a bigger, more complicated shape, you need to follow a series of steps. First, divide your big shape into simpler, symmetric shapes. Next, determine a reference axis. This is the axis you will measure from every time. Now you will measure the area of the symmetrical shapes you have created, and find the centroid of each one. Determine the distance of the height and the base of each centroid to the reference axis. Now you will multiply each symmetric shape's area by its distance from centroid to your referance axis. Add up all of the shape's areas and their centroids distances from the reference axis, and then add the individual shape's area to find the total area of the complex shape. Divide the sum of the areas and their distances by the larger objects total area.
Here are the formulas you will use to find the centroid of a complex shape.