Question

If you join all the vertices of a heptagon, how many quadrilaterals will you get?

• A. 72
• B. 36
• C. 25
• D. 35
• E. 120

Hint:

For polygons, the number of \(k\)-sided figures formed by choosing \(k\) vertices is given by the combination formula \(\binom{n}{k}\).

Answer 1

The Correct Option is B

Step 1: Understanding the problem.
We are asked to find the number of quadrilaterals that can be formed by joining the vertices of a heptagon (7-sided polygon).
Step 2: Basic combinatorial rule.
A quadrilateral is formed by choosing 4 vertices out of 7. Thus, the required number of quadrilaterals is: \[ \binom{7}{4} \]
Step 3: Calculation.
\[ \binom{7}{4} = \frac{7!}{4!(7-4)!} = \frac{7 \times 6 \times 5 \times 4}{4 \times 3 \times 2 \times 1} = 35 \]
Final Answer: \[ \boxed{35} \]