2-How to determine x-bar for a right-angle case 1?

Last Updated on September 10, 2026 by Maged kamel

How to determine x-bar for a right-angle case 1?

The difference between ccase 1and case 2 for the right-angle Triangle.

The first Moment of Area for the right-angle Triangle case 1, and how to determine the x-bar value? will be the case of the right-angled Triangle.

We have two cases: case 1, where the opposite side of the Triangle is to the left, and the base is at the bottom of the hypotenuse on the left side. In case 2, the opposite side is on the right, and the base is at the bottom of the hypotenuse on the left.

The difference between case 1 and case 2 can be shown in the next slide image.

Using a horizontal strip to get the x-bar for a right-angle case 1.

We start by using a horizontal strip to find the value of the X-bar, or the CG horizontal distance to the y-axis.
We have the X and Y axes, respectively, and the base of the Triangle. We have line AB with length b; the rise of the Triangle is h, and the inclined portion AC has the equation y = mx + C, where the slope m is equal to -h/b *x, and the intersection with the y-axis =h. The horizontal strip is shown in the next slide image.

That’s why the AC equation is Y =-( h/b) *x + h. The horizontal strip thickness is dy,, and the length is ,x, as shown in the next slide image.

First, it is good to examine the equation of the inclined line BC by substituting the value of x=0, which is point C, and checking that the corresponding y value=h when using the equation y=-(h/b)x+h). We have Y=h when x=0.

For the second point, which is point B, when the horizontal distance x and the g corresponding value is, we hav y 0, we have y = 0.

Integrate the horizontal strip to find the Area of the right-angle Triangle.

The Area of the Triangle is the sum of all the tiny horizontal strips, which we can express by integrating the strip from the start, y=0, to the end, y=h, considering the strip moving in the vertical direction.

Since the strip width is x and its height is h, we will use the relation between y and x as derived from the equation of line BC.
We estimate the Area of DA as x*dy since we integrate in the vertical direction. We will omit the x Expression by substituting its value in terms of y. The x value = (h-y)/h*(b).

Integrate the horizontal strip to find the first Moment of Area about the Y-axis.

The Expression of dA*x-strip will be represented by the first Moment of Area about the y-axis, where the x-strip is the horizontal distance from the Cg of the strip to the y-axis. The Expression of dA*x-strip is shown in the next slide image, and integration will be carried out in the vertical direction from y=0 to y=h.

The final A*x bar represents theProductt of the total Area * the horizontal CG distance from the y-axis, which will be found as, in our case=b^2*h/6, where b is the Triangle base and h is the height.

X bar for a right-angle final step.

The x-bar value will be obtained by simply dividing the first Moment oFoFor get x-bar for, x-bar, x-bar a right angle = b/3, or one-third of the base width.

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For a reliable external reference, please see Interactive Mathematics.

This is the link to the next post: X bar for a right-angle case 1- using a vertical strip.