Triangular Laminas

Basic Concepts

A lamina is a two-dimensional figure with uniform thickness.
A triangular lamina is a special type of lamina that takes the shape of a triangle.
The centre of mass of a lamina is the point at which the whole mass of the lamina can be considered as being concentrated.

The centre of mass of a triangular lamina of uniform thickness lies at the intersection of the medians of the triangle.
A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side.

For an equilateral triangle, the centre of mass is at the intersection of the medians, which also happens to be the point of intersection of the angle bisectors, perpendicular bisectors, and altitudes. It lies exactly in the centre.
For isosceles and right-angled triangles, the centre of mass also lies along the line of symmetry of the triangle.
For a scalene triangle, the centre of mass (intersection of medians) does not lie along the line of symmetry, as there isn’t one. However, it does divide each median in the ratio 2:1.

If the thickness is not uniform and varies across the lamina, the centre of mass might shift towards the region with greater mass.
The exact position of the centre of mass in such cases can be determined using the principles of moments and integration, which might be covered in higher level studies.

Understanding the concept of centre of mass of triangular laminas can be used in various fields such as engineering, construction and design for stability purposes.
It is particularly useful in the field of civil engineering where the understanding of centre of mass is vital in structural design to ensure stability and safety.