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In a heptagon, all the vertices are joined to form a triangle. How many of the triangles thus formed will have not a single side common with the heptagon?
- a)7
- b)14
- c)21
- d)28
Correct answer is option 'A'. Can you explain this answer?
Most Upvoted Answer
In a heptagon, all the vertices are joined to form a triangle. How ma...
Problem Analysis:
To solve this problem, we need to understand the properties of a heptagon and the possible triangles that can be formed using its vertices.
Properties of a Heptagon:
A heptagon is a polygon with seven sides.
Possible Triangles:
When we join all the vertices of a heptagon, we form several triangles. We need to find the number of triangles that have no side in common with the heptagon.
Solution:
To find the number of triangles that have no side in common with the heptagon, we need to count the number of triangles formed by the vertices of the heptagon.
Counting:
When we join the vertices of a heptagon, we form 7 triangles.
Explanation:
Each vertex of the heptagon is connected to two other vertices, which forms a triangle. Since there are 7 vertices in a heptagon, we have a total of 7 triangles.
Verification:
To verify our answer, we can draw a heptagon and join its vertices to form triangles. We can see that each vertex is connected to two other vertices, forming a triangle.
Conclusion:
In a heptagon, all the vertices are joined to form 7 triangles. None of these triangles have a side in common with the heptagon. Therefore, the correct answer is option A, 7.
To solve this problem, we need to understand the properties of a heptagon and the possible triangles that can be formed using its vertices.
Properties of a Heptagon:
A heptagon is a polygon with seven sides.
Possible Triangles:
When we join all the vertices of a heptagon, we form several triangles. We need to find the number of triangles that have no side in common with the heptagon.
Solution:
To find the number of triangles that have no side in common with the heptagon, we need to count the number of triangles formed by the vertices of the heptagon.
Counting:
When we join the vertices of a heptagon, we form 7 triangles.
Explanation:
Each vertex of the heptagon is connected to two other vertices, which forms a triangle. Since there are 7 vertices in a heptagon, we have a total of 7 triangles.
Verification:
To verify our answer, we can draw a heptagon and join its vertices to form triangles. We can see that each vertex is connected to two other vertices, forming a triangle.
Conclusion:
In a heptagon, all the vertices are joined to form 7 triangles. None of these triangles have a side in common with the heptagon. Therefore, the correct answer is option A, 7.
Community Answer
In a heptagon, all the vertices are joined to form a triangle. How ma...
A heptagon has 7 vertices.
Hence total number of triangles possible = 7C3 = 35
Out of these 35 triangles,
No. of triangles having 1 side common = 7 x 3 = 21
No. of triangles having 2 sides common = 7
Hence the number of triangles having no side common with the heptagon = 35 - 21 - 7 = 7.
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In a heptagon, all the vertices are joined to form a triangle. How many of the triangles thus formed will have not a single side common with the heptagon?a)7b)14c)21d)28Correct answer is option 'A'. Can you explain this answer?
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