A church steeple in the shape of a regular square pyramid needs to be reshingled. The part to be covered corresponds to the lateral area of the square pyramid. If each lateral edge measures
To find:
The lateral area of the pyramid.
Given:
A regular square pyramid as below,
and lateral edge measures
Properties Used:
A pyramid is made by connecting a base to an apex. The base is flat with straight edges, no curves, hence, a polygon and all other faces are triangles.
A regular pyramid is a pyramid whose base is a regular polygon and whose lateral edges are all congruent.
The lateral area
The total surface area
According to the Pythagorean theorem, in a right-angled triangle
In a regular pyramid, the lengths of the apothem
The perimeter of the square is four times the side.
Calculation:
From the given figure
Calculus: Early Transcendental Functions
Applied Calculus
Calculus: An Applied Approach (MindTap Course List)
Intermediate Algebra
Single Variable Calculus
Understanding Basic Statistics
Mathematical Excursions (MindTap Course List)
Single Variable Calculus: Early Transcendentals, Volume I
Calculus: Early Transcendentals
Finite Mathematics and Applied Calculus (MindTap Course List)
Precalculus: Mathematics for Calculus (Standalone Book)
Calculus (MindTap Course List)
Multivariable Calculus
Elementary Technical Mathematics
Statistics for The Behavioral Sciences (MindTap Course List)
Probability and Statistics for Engineering and the Sciences
Finite Mathematics
Essentials Of Statistics
Mathematical Applications for the Management, Life, and Social Sciences
Applied Calculus for the Managerial, Life, and Social Sciences: A Brief Approach
Essentials of Statistics for The Behavioral Sciences (MindTap Course List)
Trigonometry (MindTap Course List)
Calculus of a Single Variable
Contemporary Mathematics for Business & Consumers
Elements Of Modern Algebra
Single Variable Calculus: Early Transcendentals
Calculus: Early Transcendental Functions (MindTap Course List)
Finite Mathematics for the Managerial, Life, and Social Sciences
Research Methods for the Behavioral Sciences (MindTap Course List)
Study Guide for Stewart's Single Variable Calculus: Early Transcendentals, 8th
College Algebra (MindTap Course List)
Mathematics For Machine Technology
Study Guide for Stewart's Multivariable Calculus, 8th
Mathematics: A Practical Odyssey
Calculus (MindTap Course List)
STATISTICS F/BUSINESS+ECONOMICS-TEXT
Multivariable Calculus
Research Methods for the Behavioral Sciences (MindTap Course List)
Introduction To Statistics And Data Analysis
Statistics for Business & Economics, Revised (MindTap Course List)