Use app×
Join Bloom Tuition
One on One Online Tuition
JEE MAIN 2025 Foundation Course
NEET 2025 Foundation Course
CLASS 12 FOUNDATION COURSE
CLASS 10 FOUNDATION COURSE
CLASS 9 FOUNDATION COURSE
CLASS 8 FOUNDATION COURSE
0 votes
5.9k views
in Combinations by (46.2k points)
recategorized by

Find the number of diagonals that can be drawn by joining the angular points of a 

(i) heptagon 

(ii) a polygon of 20 sides

1 Answer

+1 vote
by (49.2k points)
selected by
 
Best answer

(i) A heptagon has seven angular points and seven sides. 

The join of two angular points is either a side or a diagonal. 

The number of lines joining the angular points = 7C2\(\frac{7\times6}{1\times}=21.\)

But the number of sides = 7 ∴ The number of diagonals = 21 – 7 = 14. 

(ii) Number of diagonals in a polygon of n sides = nC2 – n. Here, n = 20 

∴ Required number of diagonals = 20C= \(\frac{20\times19}{2\times1}-20=170.\)

Welcome to Sarthaks eConnect: A unique platform where students can interact with teachers/experts/students to get solutions to their queries. Students (upto class 10+2) preparing for All Government Exams, CBSE Board Exam, ICSE Board Exam, State Board Exam, JEE (Mains+Advance) and NEET can ask questions from any subject and get quick answers by subject teachers/ experts/mentors/students.

...