Pyramid Calculator

A Pyramid is a solid object having a polygon base, triangular sides that meet at the top. A Pyramid is a three-dimensional structure and a polyhedron.
Calculate the area, perimeter of Pyramid (Pyramid Calculator)
Regular Triangular Pyramid
Area of Base : [ ½as]
Surface Area of Pyramid : [ ½as + (3/2)sl ]
Volume of Pyramid : [ (1/6)abh ]
Apothem Length (a) :
Side Length (s) :
Slant height :
Height :
Area of Base :
Surface Area of Pyramid :
Volume of Pyramid :
Regular Square Pyramid
Area of Base : [s²]
Surface Area of Pyramid : [s² + 2sl ]
Volume of Pyramid : [(1/3)b²h ]
Side Length :
Slant height :
Height :
Area of Base :
Surface Area of Pyramid :
Volume of Pyramid :
Regular Pentagonal Pyramid
Area of Base :  [(5/2)as]
Surface Area of Pyramid :  [ (5/2)as + (5/2)sl ]
Volume of Pyramid :  [ (5/6)abh]
Apothem Length :
Side Length :
Slant height :
Height :
Area of Base :
Surface Area of Pyramid :
Volume of Pyramid :
 
Regular Hexagonal Pyramid
Area of Base : [(6/2)as ]
Surface Area of Pyramid : [ 3as + 3sl ]
Volume of Pyramid : [ abh ]
Apothem Length :
Side Length :
Slant height :
Height :
Area of Base :
Surface Area of Pyramid :
Volume of Pyramid :
Formula
Triangular Pyramid
Area of the base (A) = ½ * a * s
Surface Area of Pyramid = A + ((3/2) sl)
Volume of Pyramid = (1/6) abh
Where,
a= apothem length
s= side length
sl= slant height
abh area of base * height

Square
Area of the base (A) [s²]
Surface Area of Pyramid = [s² + 2sl]
Volume of Pyramid = [(1/3)b²h ]
Where,
s= side length
sl= slant height
b= base
h= height

Pentagonal
Area of Base : [(5/2)as]
Surface Area of Pyramid : [ (5/2)as + (5/2)sl ]
Volume of Pyramid : [ (5/6)abh]
Where,
As = area of side length
sl= slant height
abh area of base * height

Hexagonal
Area of Base: [(6/2) as]
Surface Area of Pyramid: [3as + 3sl]
Volume of Pyramid: [abh ]
Where,
As = area of side length
sl= slant height
abh area of base * height

A pyramid is a polyhedron with one face as base, a polygon and all the other faces triangles meeting at a common polygon vertex as the apex. It is a structure where the upper surfaces are triangular and converge on one point.

Examples:
Find the area, surface area and volume of a triangular pyramid with the given apothem length 2, side 3, height 4 and the slant height 5.

Step 1: Find the area of the base.
Area of the base (A) = ½ * a * s = 0.5 * 2 * 3 = 3.

Step 2: Find the surface area of pyramid.
Surface Area of Pyramid = A + ((3/2) sl) = 3 + ((3/2) * 3 * 5) = 3 + (1.5 * 15) = 3 + 22.5 = 25.5.

Step 3: Find the volume of pyramid.
Volume of Pyramid = (1/6) abh = (1/6) * 2 * 3 * 4 = 0.17 * 24 = 4.08.

Find the area, surface area and volume of a Square pyramid with the given side length3, height 4 and the slant height 5.

Step 1: Find the area of the base.
Area of the base (A) [s²] = 32  = 9

Step 2: Find the surface area of pyramid.
Surface Area of Pyramid = [s² + 2sl] = 32 +2*5= 9+10 = 9 +2*5*3 =9+30 = 39

Step 3: Find the volume of pyramid.
Volume of Pyramid = [(1/3)b²h ] = [(1/3)*92 *4] = (1/3)*9*4 = 36/3 = 12

Find the area, surface area and volume of a Pentagonal pyramid with the given side apothem length 2, side 3, Slant height 4 and height 5.

Step 1: Find the area of the base.
Area of Base : [(5/2)as] = [ (5/2)2*3]= 5/2*6= 2.5*6= 15

Find the surface area of pyramid.
Surface Area of Pyramid : [ (5/2)as + (5/2)sl ]= 15+(2.5*3*4) = 15+ (2.5*12) =15+30 = 45

Find the volume of pyramid.
Volume of Pyramid : [ (5/6)abh] = (5/6) 2*3*5=  (5/6) * 30 = 0.833 *30 = 25 \

Find the area, surface area and volume of a Hexagonal pyramid with the given side apothem length 2, side 3, Slant height 4 and height 5.

Step 1: Find the area of the base. Area of Base:  [(6/2) as] = [(6/2) 2*3= (6/2) *6 = 3*6 = 18

Find the surface area of pyramid.
Surface Area of Pyramid:  [3as + 3sl] = [(3*2*3) + (3*3*4)] = 18+36 = 54

Find the volume of pyramid.
Volume of Pyramid:  [abh ] = 2*3*5 = 30