Buzz
A pyramid is a polyhedron formed by connecting a polygonal base and a point, called the apex. Unlike other 3D shapes such as cubes, rectangular prisms, and prisms, a pyramid's area consists of both lateral area and total surface area. Discover how to calculate these areas without delving into the underlying principles.
How is the Pyramid Area Calculated?
Pyramid Area Formulas
Regular Pyramid
Given:
Sl is the lateral surface area
p is the base perimeter's half
d is the slant height of the regular pyramid
- Statement: The lateral area of a regular pyramid equals the base perimeter multiplied by the slant height.
Regular Quadrilateral Pyramid
- Lateral area calculation method:
Sl = Sum of the side faces' areas (Total area of 4 triangles)
- Total Surface Area Calculation for Pyramids
Practical Problems on Pyramid Area Calculation
Exercise 1. Find the lateral area of pyramid SABCD with a square base of side 20 cm, and lateral edges 10 cm long.
Exercise 2. Calculate both the lateral area and total surface area of a regular quadrilateral pyramid SABCD with a base edge of 5 m and height of 6 m.
Exercise 3. Determine the lateral area of a regular pyramid SABC with base edge a = 12 dm and height h = 8 dm.
* Tips for solving the exercises:
In this article, we've helped you reinforce and review the formulas for calculating pyramid areas, including both total surface area and lateral area. Additionally, we've provided some simple calculation exercises to guide you in solving and presenting your work accurately and scientifically. We hope you achieve high scores in your upcoming math exams and tests. It's also crucial for you to master the calculation of rectangle areas, as this is fundamental knowledge you need to grasp.
Another related problem involving pyramids is the formula for calculating pyramid volume, which is also a concept you should pay attention to and remember. If you have any questions about the concept of what an equilateral triangular pyramid is or any related knowledge about regular pyramids, you can find references here.
