Pyramid is one where the surface of outer area looks triangular and it converges at that point. They are congruent .Square pyramid is a pyramid in which the base of pyramid looks to be square. The most popular form of square pyramid is Johnson square pyramid. If the apex is perpendicularly on top of the center of the square, it will have C4v symmetry.
what is square pyramid
Formulae for square pyramid:
Volume of a square pyramid V = `1/3` (Ah)
= `1/3` a2 h (Area of square = a2)
Height of square pyramid h = (3 * V) / a2
Where, A -----> area of base of a pyramid
V -----> Volume of a pyramid
a -----> Side length
what is square pyramid
Surface area of a square pyramid = side2 + 2 x side x length
what is square pyramid
Example problems for square pyramid:
ExampleExample 1:
Find the surface area of a square based pyramid with the given sides 6 cm, height 7 cm, and the slant height 8 cm.
Solution:
Formula:
Surface area of a square pyramid = side2 + 2 x side x length
Given:
Side = 6 cm, length = slant height = 8cm
Surface area = (6)2 + 2 x 6 x 8
= 36 + 96
= 132
The Surface area of square pyramid is 132 square cm.
ExampleExample 2:
Find the volume of square pyramid for a given dimensions base = 5cm, height = 6cm.
Solution:
Formula:
Volume of the pyramid = `1/3` * Area of base * height.
Given:
Base = 5cm, height = 6cm.
Area of base = b2
Volume = `1/3` * 52 * 6 cm3
= `1/3` * (150) cm3
= 50 cm3
The Final answer is 50 cm3.
ExampleExample 3:
Find the volume of the square pyramid whose base area is 16 cm and height is 12 cm.
Solution:
Formula:
Volume of the pyramid = `1/3` * B*h
Given:
Base area is 16 cm and height is 12 cm.
Volume of the pyramid = `1/3` * 16 * 12
= `1/3` * 192
= `192/3`
= 64 cm3
Practice problems:
Problem 1:
Find the volume of square pyramid for a given dimensions base = 2cm, height =3cm.
Solution:
Volume of a square pyramid is 4cm3.
Problem 2:
Find the volume of the square pyramid whose base area is 15 cm and height is 13 cm.
Solution:
Volume of a square pyramid is 65cm3.
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