a.
To find: The number of diagonals a
A triangle has
Given:
A triangle.
Concept used:
Here, we are using the formula:
Diagonal of a
(Where, “n” is side)
Calculation:
We know that,
A triangle has
So, diagonals of a triangle =
(Where, “n” is side)
➜
➜
Conclusion: Hence, a triangle has
b.
To find: The number of diagonals a quadrilateral can have
A quadrilateral has
Given:
A quadrilateral.
Concept used:
Here, we are using the formula:
Diagonal of a polygon =
(Where, “n” is side)
Calculation:
We know that,
A quadrilateral has
So, diagonals of a quadrilateral =
(Where, “n” is side)
➜
➜
Conclusion: Hence, a quadrilateral has
c.
To find: The number of diagonals a five-sided polygon can have
A five-sided polygon have
Given:
Afive-sided polygon
Concept used:
Here, we are using the formula:
Diagonal of a polygon =
(Where, “n” is side)
Calculation:
So, diagonals of a five-sided polygon =
(Where, “n” is side)
➜
➜
Conclusion: Hence, a five-sided polygon have
d.
To find: The number of diagonals a six-sided polygon can have
A six-sided polygon have
Given:
A five-sided polygon
Concept used:
Here, we are using the formula:
Diagonal of a polygon =
(Where, “n” is side)
Calculation:
So, diagonals of a six-sided polygon =
(Where, “n” is side)
➜
➜
Conclusion: Hence, a six-sided polygon have
e.
To find: The number of diagonals meet at one vertex of a polygon with n sides.
The number of diagonals is
Given:
A polygon have n sides.
Concept used:
Here, we are using the formula:
Diagonal of a polygon =
(Where, “n” is side)
Explanation:
We know that,
From each vertex we can draw
So, the total number of diagonals is
Conclusion: Hence, the number of diagonals is
f.
To find: The number of vertices an n-sided polygon can have
The number of vertices is n
Given:
An n-sided polygon.
Explanation:
An n-sided polygon can have n vertices and from each vertex we can draw
Conclusion: Hence, the number of vertices is n
g.
To find: The number of diagonals an n-sided polygon can have
The number of diagonals is
Given:
An n-sided polygon.
Explanation:
An n-sided polygon can have n vertices and from each vertex we can draw
So, the total number of diagonals =
Conclusion: Hence, the number of diagonals is
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- Elementary Geometry For College Students, 7eGeometryISBN:9781337614085Author:Alexander, Daniel C.; Koeberlein, Geralyn M.Publisher:Cengage,Elementary Geometry for College StudentsGeometryISBN:9781285195698Author:Daniel C. Alexander, Geralyn M. KoeberleinPublisher:Cengage Learning