how to find the center of an equilateral triangle

Download Article

The center of gravity, or centroid, is the signal at which a triangle's mass will balance. To help visualize this, imagine y'all have a triangular tile suspended over the tip of a pencil. The tile will balance if the pencil tip is placed at its center of gravity. Finding the centroid might be necessary in various pattern and engineering applications, and can be found by using uncomplicated geometry.

ane
Discover the midpoint of one side of the triangle. To find the midpoint, measure the side, and divide the length in half. Label the midpoint A.
- For example, if one side of the triangle is x cm long, the midpoint will be at 5 cm, since $10/2=5$ .
two
Observe the midpoint of a 2d side of the triangle. Measure the length of the side, and separate the length in half. Label the midpoint B.
- For example, if the side of the triangle is 12 cm long, the midpoint will be at 6 cm, since $12/2=6$ .
Advertisement
three
Draw a line from the midpoint of each side to its opposite vertex. These two lines are the median of each side. ^[1]
- A vertex is the point at which two sides of a triangle encounter.
4
Draw a betoken where the 2 medians intersect. This point is the triangle'southward center of gravity, as well called the centroid, or eye of mass. ^[2] ^[3]
- The center of gravity is where the three medians intersect, only since the medians but intersect in ane point, you can utilize a shortcut and observe the center of gravity by only finding the intersection of two medians.
Advertisement

1

Draw a median of your triangle. Recollect, the median is a line drawn from the midpoint of a side to the opposite vertex. Yous tin employ any median in the triangle.
2
Measure out the length of the median. Make certain the measurement is exact.
- For example, you might have a median that is 3.vi cm long.
3
Carve up the length of the median into thirds. To do this, divide the length by three. Over again, make an exact calculation. If you round, you will not discover the eye of gravity.
- For example, if your median is 3.6 cm long, you would divide 3.6 by 3:
  $iii.6cm/iii=1.2cm$ , and so ⅓ of the median is 1.ii cm.
4
Marker a point on the median ⅓ from the midpoint. This point is the triangle'southward centroid, which will always divide a median into a 2:1 ratio; that is, the centroid is ⅓ the median's distance from the midpoint, and ⅔ the median's distance from the vertex.^[iv]
- For example, on a median that is 3.6 cm long, the centroid will be 1.ii cm upward from the midpoint.
Advertizement

1
Determine the coordinates of the 3 vertices of the triangle. This method only works if y'all are working with a coordinate plane. The coordinates may already exist given, or you may take a triangle fatigued on a graph without the coordinates labeled. Remember that coordinates should be listed $(x,y)$ .
- For case, you lot might exist given triangle PQR, and you need to observe and label signal P (3, 5), point Q (4, 1), and R (1, 0).
two
Add the value of the x-coordinates. Remember to add together all 3 coordinates. You lot will not summate the correct center of gravity if you only utilize two coordinates.
- For example, if your three x-coordinates are 3, four, and 1, add these 3 values together: $iii+iv+1=8$ .
iii
Add together the value of the y-coordinates. Call back to add all iii coordinates.
- For case, if your 3 y-coordinates are 5, ane, and 0, add these three values together: $five+ane+0=6$ .
four

Notice the average of the 10- and y-coordinates. These coordinates will correspond to the triangle's center of gravity, also known every bit the centroid or heart of mass.^[5] To discover the average, divide the sum of the coordinates by 3.
5
Plot the heart of gravity on the triangle. The center of gravity, or centroid, is the average of the 10- and y-coordinates.
- In the example problem, the center of gravity is the point $(viii/three,2)$ .
Advertising

Add New Question

Question

The length of a rectangle is x units and the width is x-5. How do I detect an equation for the perimeter and expanse of the rectangle?

For the perimeter, add the iv sides together and simplify. For the area, multiply the length by the width.
Question

Is the middle of gravity of triangular cardboard outside or on the torso?

The center of gravity is e'er within the triangle.
Question

How can I determine the center of gravity of an Isoceles triangle without knowing the mass?

The horizontal coordinate will be half of the base, and the vertical volition be 1 third of the height.
Question

How do I calculate the center of an isosceles triangle?

The heart of gravity of an isosceles triangle is determined in the aforementioned way as with whatever other triangle, as shown above. Thus, draw 2 (or iii) medians, and their betoken of intersection is the centre of gravity.
Question

What is the heart of gravity of a triangular metal plate with one side 8 cm and other side half dozen cm?

That's not plenty information to find the center of gravity. You accept to be able to define (depict) the triangle before you can find the c.o.g.

Inquire a Question

200 characters left

Include your email address to go a message when this question is answered.

Submit

Video

It does not affair which side you select, the middle of gravity will exist at the aforementioned signal. If you perform this procedure on all three sides, the lines will cantankerous at a single point.

Thanks for submitting a tip for review!

Advert

About This Article

Commodity Summary X

To calculate the middle of gravity of a triangle, kickoff by drawing a line from the midpoint of any ane of the sides to the contrary vertex to create a median. Next, measure the median and dissever it into thirds. For example, if the median is 3.half dozen cm long, marker the spots that are ane.2 cm and 2.4 cm along the median, starting from the midpoint. The spot that'southward 1.ii inches from the midpoint is the centroid, or the middle of gravity of the triangle. To acquire more, like how to find the centre of gravity of a triangle using intersecting medians, scroll down.

Did this summary assist you?

Thanks to all authors for creating a page that has been read 257,315 times.