The Series of Sketches Below Starts with an Equilateral Triangle

question 86

Essay

The series of sketches below starts with an equilateral triangle having sides of length 1 (one). In the following
steps, equilateral triangles are constructed by joining the midpoints of the sides of the preceding triangle.
Develop a formula for the area of the nth new triangle. Use math induction to prove your answer.

---

Definitions:

Election Petition

A formal request, often filed by employees or labor organizations, seeking an election to establish or decertify a labor union as the representative of a group of workers.

Union Instrumentality

The effectiveness of a labor union in achieving desired outcomes or benefits for its members, such as higher wages or better working conditions.

National Labor Relations Act

A foundational statute in United States labor law that protects the rights of employees to organize, form unions, and engage in collective bargaining.

Supervisors

Individuals in an organization responsible for overseeing the work of employees and ensuring that the work is completed efficiently and effectively.