a.
To calculate: The measure of
a.
Answer to Problem 8PSB
The measure of angle E is
Explanation of Solution
Given information:
A pentagon with center O.
Side EN = 12 cm.
Formula used:
Exterior angle at E is
n = number of sides.
Calculation:
m∠ EON or exterior angle at E is
b.
To find: The measure of angle NOM if side EN is 12 cm.
b.
Answer to Problem 8PSB
The measure of angle NOM is
Explanation of Solution
Given information:
A pentagon with center O.
Side EN = 12 cm.
Formula used:
Exterior angle at T is
n = number of sides.
Calculation:
m∠ NOT
c.
To calculate: The length of side
c.
Answer to Problem 8PSB
The length of side
Explanation of Solution
Given information:
A pentagon with center O.
Side EN = 12 cm.
Formula used:
Calculation:
m∠ NOT
In ΔNOM,
d.
To find: The area of
d.
Answer to Problem 8PSB
The area of triangle NOT is
Explanation of Solution
Given information:
A pentagon with center O.
Side EN = 12 cm.
Formula used:
Area of triangle:
b = base of triangle
h = height of triangle
Calculation:
m∠NOT
In ΔNOM,
NT = 12 cm
Area of triangle NOT
Area of triangle NOT
Area of triangle NOT
e.
To find: The area of pentagon.
e.
Answer to Problem 8PSB
The area of pentagon can be calculated by multiplying area of triangle NOT by 5.
Explanation of Solution
Given information:
A pentagon with center O.
Side EN = 12 cm.
Formula used:
Area of triangle:
b = base of triangle
h = height of triangle
m∠ NOT
In ΔNOM,
NT = 12 cm
Area of triangle NOT
Area of triangle NOT
Area of triangle NOT
Area of pentagon is sum of areas of triangles NOT , TOA , AOP , POE and EON.
All five triangles are identical and have same area as triangle NOT.
Area of Pentagon
Chapter 9 Solutions
Geometry For Enjoyment And Challenge
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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