(a)
To find: The length of the sides
(a)
Answer to Problem 23WE
The length of the sides
Explanation of Solution
Given information:
The length of
Calculation:
Use the Pythagoras theorem in
Further simplify,
So, the length of the side
The length of the side
So, the length of the side
The side
Further simplify,
So, the length of the side
Therefore, the length of the sides
(b)
To find: The lateral area and volume of the pyramid.
(b)
Answer to Problem 23WE
The lateral area and volume of the pyramid is equal to
Explanation of Solution
Given information:
The length of
Calculation:
The formula for the lateral area of the pyramid is the half the product of the perimeter of the base and the slant height of the pyramid.
The perimeter of the base is the three times the sum of the length of side
As found in part(a), the length
Substitute
So, the lateral area of the pyramid is equal to
The formula for the volume of the pyramid is equal to the one third of the product of area of base and the length
The base of the pyramid is equilateral triangle with side equal to
The area of the equilateral triangle is:
As found in part(a), the length
Substitute
So, the volume of the pyramid is equal to
Therefore, the lateral area and volume of the pyramid is equal to
Chapter 12 Solutions
McDougal Littell Jurgensen Geometry: Student Edition Geometry
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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