Pyramid

Pyramid

The pyramid is a three-dimensional figure with several flat faces that consists of:

  • Base: A simple polygon located at the bottom of the pyramid. It can be a triangle, square, pentagon or any other polygon with straight sides. Depending on the base, they can be regular pyramids (the sides of the base polygon have the same length) or irregular pyramids (the sides of the base polygon have different lengths).
  • Lateral faces: Triangles that join the base on one of its sides. The number of lateral faces is equal to the number of sides of the base.
  • Vertex: The upper point where all the vertices (corners) of the lateral faces meet.

Examples of pyramids in the real world:

  • The pyramids of Egypt are a famous example of regular quadrangular pyramids.
  • Space Rockets: Some rocket designs have a shape similar to a pyramid.

 

 

 

Volume formulas

Square pyramid

Volume of a pyramid is equal to one-third of the area of its base multiplied by its heigh
 a – lenght base side
H –  perpendicular height, height of the pyramid
B – area of ​​pyramid base
Pyramid
H –  perpendicular height, height of the pyramid
B – area of ​​pyramid base
a – lenght base side

Surface area formulas

Square pyramid

SA= LSA +  B

A = B + 1/2 x P x l

P = 4a

LSA =1/2 x P x l=

= 1/2 x 4a x l =2al

B = a2

Lateral surface area of a pyramid (LSA) = Sum of areas of the lateral surfaces of the pyramid
 SA – surface area

LSA – lateral surface area

B – bases area

a -base´s side lenght
H –  perpendicular height, height of the pyramid
B – area of ​​pyramid base

P –  perimeter of the base

l –  slant length of the lateral sides (lenght base to vertex, apex)
Triangular Pyramid

SA= LSA +  B

SA = B + 1/2 x P x l

LSA =1/2 x P x l

Bases area  =  polygon area

Lateral surface area of a pyramid (LSA) = Sum of areas of the lateral surfaces (triangles) of the pyramid
SA – surface area

LSA – lateral surface area

B – bases area

P –  base perimeter

H –  perpendicular height, height of the pyramid
a -base´s side lenght

l (m) –  slant length of the lateral sides.

Bases area  = polygon area

h – height of the triangle