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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)

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: surface area and volume of a triangular pyramid calculator**

**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 right square (right rectangular) pyramid with the given side length3, height 4 and the slant height 5.**

**Step 1:** Find the area of the base. (right rectangular pyramid calc: find a)

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. (right rectangular pyramid calc: find v)

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**