Maths Formulas

Pyramid Formula

A pyramid is a polyhedron that has a polygonal base and triangles for sides. The three main parts of any pyramid are the apex, face, and base. The base of a pyramid may be of any shape such as triangle, square, pentagon. Faces are in the shape of an isosceles triangle. Apex is a point at the top of the pyramid where all the triangle of the pyramid meets. Let us now discuss the different pyramid formula in detail.

What is a Pyramid?

A 3-dimensional shape formed by joining all the corners of a polygon to a central point or apex is named as a pyramid. The slant height is the diagonal height from the center of one of the base edges to the apex denoted by l. Height is the perpendicular distance from the apex to the base. Height is denoted by h.

Pyramid Formula

Pyramid Formula

1] Surface area of the Pyramid

The lateral surface area of a regular pyramid is the sum of the areas of the lateral faces of the pyramid.

\(L.S.A. = \frac{1}{2} × p × l\)

p the perimeter of the base
l slant height

2] Total Surface Area of a Regular Pyramid

It is the sum of the areas of lateral faces of the pyramid and base of the pyramid.

\(T.S.A.= \frac{1}{2} × p × l + B\)

p the perimeter of the base
l slant height
B the area of the base

3] Volume of the Pyramid

Volume of a 3 -dimensional solid is the amount of space occupies by the solid.

The volume of a Pyramid=\(\frac{1}{2} × Base Area × Height\)

Types of Pyramid

1] Square Pyramid

A square pyramid has a square base, triangular faces as 4 and an apex. The Square Pyramid formulas are,

  • Base Area of a Square Pyramid = b2
  • Surface Area of a Square Pyramid = 2 × b × s +b2
  • Volume of a Square Pyramid=\(\frac{1}{3}\) × b2 × h
b base length
s slant height
h height

2] Triangular Pyramid

A triangular pyramid is a pyramid, which has triangular faces, and a triangular base. The Triangular Pyramid formulas are,

  • Base Area of a Triangular Pyramid=\(\frac{1}{2} × a × b\)
  • Surface Area of a Triangular Pyramid=\(\frac{1}{2} ×  a × b+\frac{3}{2} × b ×s\)
  • The volume of a Triangular Pyramid=\(\frac{1}{6} × a × b × h\)
a apothem length
b base length
s slant height
h height

3] Pentagonal Pyramid

The Pentagonal pyramid has a pentagonal base, triangular faces as 5 and an apex. The Pentagonal Pyramid Formulas are,

  • Base Area of a Pentagonal Pyramid=\(\frac{5}{2} × a × b\)
  • Surface Area of a Pentagonal Pyramid=\(\frac{5}{2} (a × b + b × s)\)
  • The volume of a Pentagonal Pyramid=\(\frac{5}{6} × a × b × h\)

Solved Example for Pyramid Formula

Q.1: Find the volume of a regular square pyramid with base sides 10 cm and altitude 18 cm.

Solution: Volume of a pyramid is,

\(V=\frac{1}{3}Base area × h\)

base area= 10 × 10 = 100  cm2.

\(V= \frac{1}{3} × (100) × (18) = 600\)

Therefore, the volume of the regular square pyramid is 600 cm3

Q.2: Find the lateral surface area of a regular pyramid with a triangular base if each edge of the base measures 88 cm and the slant height is 55 cm.

Solution: The perimeter of the base is the sum of the sides.

Perimeter of the base = 3 × (8) = 24 cm

L.S.A. =\( \frac{1}{2} p × l  = \frac{1}{2} (24) × (5) = 60  cm^2\)

Share with friends

Customize your course in 30 seconds

Which class are you in?
5th
6th
7th
8th
9th
10th
11th
12th
Get ready for all-new Live Classes!
Now learn Live with India's best teachers. Join courses with the best schedule and enjoy fun and interactive classes.
tutor
tutor
Ashhar Firdausi
IIT Roorkee
Biology
tutor
tutor
Dr. Nazma Shaik
VTU
Chemistry
tutor
tutor
Gaurav Tiwari
APJAKTU
Physics
Get Started

1
Leave a Reply

avatar
1 Comment threads
0 Thread replies
4 Followers
 
Most reacted comment
Hottest comment thread
1 Comment authors
KUCKOO B Recent comment authors
  Subscribe  
newest oldest most voted
Notify of
KUCKOO B
Guest
KUCKOO B

I get a different answer for first example.
I got Q1 as 20.5
median 23 and
Q3 26

Yashitha
Guest
Yashitha

Hi
Same

virat
Guest
virat

yes

Customize your course in 30 seconds

Which class are you in?
No thanks.