To get the best deal on Tutoring, call 1-855-666-7440 (Toll Free)
Top

Pyramid Calculator
Top
Pyramid Calculator is used to area of base, surface area and volume for triangular and square pyramid.

Triangular pyramid is one type of three dimensional figure. It has a four vertices. Three vertices are at the base of pyramid and another vertex is on top. Vertices are nothing, its a corner points of the pyramid.
Triangular Pyramid
Square pyramid is one type of three dimensional figure. Depending upon the base shape of pyramid, the name of the pyramid will be varied. For example, if the base of the pyramid is a square shape, that pyramid is know as square pyramid.

Square Pyramid
 

Step by Step Calculation

Back to Top
Step 1 :  

Square Pyramid Formula:


 


Area of Square Base = s2


 


Surface Area of Square Pyramid = s2 + 2sl


 


Volume of Square Pyramid = $\frac{1}{3}$ b2h


 


Where,


 


s (b) = side length


 


l = slant height


 


h = height


 


Triangular Pyramid Formula:


 


Area of Triangular Base = $\frac{1}{2}$ as


 


Surface Area of Triangular Pyramid = $\frac{1}{2}$as + $\frac{3}{2}$ sl


 


Volume of Triangular Pyramid = $\frac{1}{6}$ abh


 


Where,


 


a = apothem


 


s = side length


 


l = slant height


 


h = height



Step 2 :  

Put the values in the formula and calculate it further.



Example Problems

Back to Top
  1. Square pyramid is having side length 5 cm, height 7 cm and slant height 6 cm. Find the area of base, volume and surface area of square pyramid.


    Step 1 :  

    Given:


     


    s = 5 cm


     


    h = 7 cm


     


    l = 6 cm


     


    Square Pyramid Formula:


     


    Area of Base = s2


     


    Surface Area of Square Pyramid = s2 + 2sl


     


    Volume of Square Pyramid = $\frac{1}{3}$ b2h



    Step 2 :  

    Put the values in the formula and calculate it further.


     


    Area of Square Base = 52 cm


     


                       = 25 cm2


     


    Surface Area of Square Pyramid = 52 + 2 * 5 * 6


     


                                                 = 25 + 60


     


                                                  = 85 cm2


     


    Volume of Square Pyramid = $\frac{1}{3}$ 52 * 7


     


                                          = 58.33 cm3



    Answer  :  

    Area of Square Base = 25 cm2

     

     

     

     

     

     

     

    Surface Area of Square Pyramid = 85 cm2

     

     

     

     

     

     

     

    Volume of Square Pyramid = 58.333 cm3



  2. Triangular Pyramid has height 8 cm, slant height 6 cm, apothem 7 cm and side length is 5 cm. Calculate Area of base, surface area and volume of triangular pyramid.


    Step 1 :  

    Given:


     


    s = 5 cm


     


    l = 6 cm


     


    a = 7 cm


     


    h = 8 cm


     


    Triangular Pyramid Formula:


     


    Area of Triangular Base = $\frac{1}{2}$ as


     


    Surface Area of Triangular Pyramid = $\frac{1}{2}$as + $\frac{3}{2}$ sl


     


    Volume of Triangular Pyramid = $\frac{1}{6}$ abh



    Step 2 :  

    Put the values in the formula and calculate it further.


     


    Area of Triangular Base = $\frac{1}{2}$ * 5 * 7


     


                       = 17.5 cm2


     


    Surface Area of Triangular Pyramid = $\frac{1}{2}$ * 5 * 7 + $\frac{3}{2}$ * 5 * 6


     


                                                      = 62.5 cm2


     


    Volume of Triangular Pyramid = $\frac{1}{6}$ * 7 * 6 * 8


     


                                              = 56 cm3



    Answer  :  

    Area of Triangular Base = 17.5 cm2

     

    Surface Area of Triangular Pyramid = 62.5 cm2

     

    Volume of Triangular Pyramid = 56 cm3



More Pyramid Calculator
Volume of a Pyramid Calculator Surface Area of a Pyramid Calculator
*AP and SAT are registered trademarks of the College Board.