Subscribe to our YouTube channel for the latest videos, updates, and tips.


Pyramid

What is pyramid?

A pyramid is a solid bounded by plane faces ; one of its faces is a polygon of any number of sides and the other faces are triangles whose bases are the sides of the polygon and which meet at a common point outside the plane of the polygon.

The plane face which is a polygon is called the base of the pyramid and the triangular faces are its lateral faces. The common point at which the lateral faces meet is called its vertex. The straight lines in which adjacent faces intersect are called the edges (or lateral edges) of the pyramid. The perpendicular distance from the vertex to the plane of the base is called the height (or altitude) of the pyramid. Evidently, a pyramid will have n lateral faces if its base is a polygon of n sides. A pyramid is said to be triangular, quadrangular, pentagonal or hexagonal according as its base is a triangle, quadrilateral, pentagon or hexagon.

pyramid




A pyramid has been displayed in given figure. The base of the pyramid is the pentagon JKLMN, its vertex is P; its lateral faces are the plane triangles PJK, PKL etc. and PJ, PK etc. are its edges. If PO be perpendicular to the plane of the base JKLMN then its height is PO.






Right Pyramid: If the base of a pyramid is a regular polygon and perpendicular drawn from its vertex to the base passes through the centre of the base (i.e. the centre the circumscribed or the inscribed circle of the regular polygon) then the pyramid is called a right pyramid.


The lateral faces of a right pyramid are congruent isosceles triangles. The length of the line joining the vertex to the centre of the base is called height of the right pyramid. The length of the perpendicular drawn from the vertex to any side of base is called the slant height of the right pyramid. Evidently, the slant height is the same for each lateral face of a right pyramid and each slant height bisects the corresponding side of the base. The sum of the areas of the lateral faces of a right prism is called its slant surface.

right pyramid


A right pyramid has been shown in the given figure. It’s base is the regular pentagon ABCDE and P is its vertex; PO is the height of the right pyramid, P0 being the centre of the base; PAB, PBC etc. are its lateral faces which are all isosceles triangles having equal area. If PN bisects AE at right angles, then PN is the slant height of the right pyramid.





Let a be the length of each side of the base of a right pyramid. If h be the height and 1, the slant height of the right pyramid, then

1. The area of the slant surface of the right pyramid

= 1/2 a ∙ l + 1/2 a ∙ l + 1/2 a ∙ l + ……..

= 1/2 ( a + a + a + ……) ∙ l

= 1/2 × perimeter of the base × slant height;


2. Area of whole surface of the right pyramid = area of its slant surface + i.e. area of its base

3. Volume of a right pyramid = 1/3 × area of the base × height.


 Mensuration




11 and 12 Grade Math 

From Pyramid to HOME PAGE




Didn't find what you were looking for? Or want to know more information about Math Only Math. Use this Google Search to find what you need.



New! Comments

Have your say about what you just read! Leave me a comment in the box below. Ask a Question or Answer a Question.




Share this page: What’s this?

Recent Articles

  1. 8 Times Table | Multiplication Table of 8 | Read Eight Times Table

    May 18, 25 04:33 PM

    Printable eight times table
    In 8 times table we will memorize the multiplication table. Printable multiplication table is also available for the homeschoolers. 8 × 0 = 0 8 × 1 = 8 8 × 2 = 16 8 × 3 = 24 8 × 4 = 32 8 × 5 = 40

    Read More

  2. Worksheet on Average | Word Problem on Average | Questions on Average

    May 17, 25 05:37 PM

    In worksheet on average interest we will solve 10 different types of question. Find the average of first 10 prime numbers. The average height of a family of five is 150 cm. If the heights of 4 family

    Read More

  3. How to Find the Average in Math? | What Does Average Mean? |Definition

    May 17, 25 04:04 PM

    Average 2
    Average means a number which is between the largest and the smallest number. Average can be calculated only for similar quantities and not for dissimilar quantities.

    Read More

  4. Problems Based on Average | Word Problems |Calculating Arithmetic Mean

    May 17, 25 03:47 PM

    Here we will learn to solve the three important types of word problems based on average. The questions are mainly based on average or mean, weighted average and average speed.

    Read More

  5. Rounding Decimals | How to Round a Decimal? | Rounding off Decimal

    May 16, 25 11:13 AM

    Round off to Nearest One
    Rounding decimals are frequently used in our daily life mainly for calculating the cost of the items. In mathematics rounding off decimal is a technique used to estimate or to find the approximate

    Read More