To find: The area of the shaded region.
Answer to Problem 32PPS
The required area of the regular
Explanation of Solution
Given:
The given diagram is shown in Figure 1
Figure 1
Calculation:
Consider the formula for the area of the regular
Consider the isosceles triangle with the vertex at the centre of the pentagon with the segment that bisects the central
Figure 2
Find the tangent ratio with the help of the apothem as,
The area with the help of side length and the apothem is obtained as,
The area of the regular 3 gon is calculated as,
The area of the regular 4 gon is calculated as,
The area of the regular 5 gon is calculated as,
The area of the regular 6 gon is calculated as,
Then, the area of the composite figure is,
Chapter 11 Solutions
Geometry, Student Edition
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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