To find: the lateral and surface area
Answer to Problem 6PPS
The surface area of the pentagonal pyramid is
Explanation of Solution
Given:
Formula used:
The lateral area L of a pentagonal pyramid is
The surface area S of a pentagonal pyramid is S = L + B
Calculation:
The given figure is a pentagonal pyramid.
The objective is to find the lateral and surface area of the pentagonal pyramid.
Find the lateral area of the pentagonal pyramid as follows:
The side of the square is 10 yd.
The perimeter P of the pentagon is P = 5 (side)
Substitute side = 10 in the perimeter formula to find the perimeter of the pentagon.
Thus,
The slant height of the pentagonal pyramid is 12 yd.
Substitute P = 50 and l = 12 in the lateral surface area to find the lateral surface area of the pentagonal pyramid.
Therefore, the lateral area of the pentagonal pyramid is
Find the surface area of the pentagonal pyramid as follows:
The area B of the base is
Substitute B = 260 and L = 300 in the surface area formula to find the surface area of the pentagonal pyramid.
Conclusion:
Therefore, the surface area of the pentagonal pyramid is
Chapter 12 Solutions
Pre-Algebra Student Edition
Additional Math Textbook Solutions
Algebra and Trigonometry
Intermediate Algebra (7th Edition)
College Algebra with Modeling & Visualization (5th Edition)
Linear Algebra with Applications (2-Download)
Elementary and Intermediate Algebra
Elementary Algebra
- Algebra and Trigonometry (6th Edition)AlgebraISBN:9780134463216Author:Robert F. BlitzerPublisher:PEARSONContemporary Abstract AlgebraAlgebraISBN:9781305657960Author:Joseph GallianPublisher:Cengage LearningLinear Algebra: A Modern IntroductionAlgebraISBN:9781285463247Author:David PoolePublisher:Cengage Learning
- Algebra And Trigonometry (11th Edition)AlgebraISBN:9780135163078Author:Michael SullivanPublisher:PEARSONIntroduction to Linear Algebra, Fifth EditionAlgebraISBN:9780980232776Author:Gilbert StrangPublisher:Wellesley-Cambridge PressCollege Algebra (Collegiate Math)AlgebraISBN:9780077836344Author:Julie Miller, Donna GerkenPublisher:McGraw-Hill Education