Question
Download Solution PDFConsider a regular polygon with 10 sides. What is the number of triangles that can be formed by joining the vertices which have no common side with any of the sides of the polygon?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFFormula used:
Triangle having no side common with those of the polygon =
\(\rm \frac{n(n-4)(n-5)}{6}\)
n is the sides of the polygon.
Calculation:
Here n = 10
Triangle having no side common with those of the polygon
= \(\rm \frac{10(10-4)(10-5)}{6}\)
= \(\rm \frac{10\times 6\times 5}{6}\)
= 50
∴ The number of triangles is 50.
Last updated on May 30, 2025
->UPSC has released UPSC NDA 2 Notification on 28th May 2025 announcing the NDA 2 vacancies.
-> A total of 406 vacancies have been announced for NDA 2 Exam 2025.
->The NDA exam date 2025 has been announced for cycle 2. The written examination will be held on 14th September 2025.
-> Earlier, the UPSC NDA 1 Exam Result has been released on the official website.
-> The selection process for the NDA exam includes a Written Exam and SSB Interview.
-> Candidates who get successful selection under UPSC NDA will get a salary range between Rs. 15,600 to Rs. 39,100.
-> Candidates must go through the NDA previous year question paper. Attempting the NDA mock test is also essential.