The volume of the pyramid, the lateral area of the pyramid and the Total surface area of the pyramid are 120.68 cubic units, 110.89 square units, and 174.88 square units, respectively.
What is Geometry?
It deals with the size of geometry, region, and density of the different forms both 2D and 3D.
All the edges of a regular square pyramid have a length of 8.
Then the height of the triangle will be
[tex]h^2 = 8^2 -( \dfrac{8}{\sqrt2})^2\\\\h \ \ = 5.66[/tex]
The volume of the pyramid will be
[tex]\rm Volume = \dfrac{1}{3}*8*8*5.66\\\\Volume = 120.68[/tex]
The lateral area of the pyramid will be
[tex]\rm Lateral \ area = l\sqrt{(\dfrac{w}{2})^2 + h^2} +w\sqrt{(\dfrac{l}{2})^2+ h^2}\\\\ Lateral \ area = 8\sqrt{(\dfrac{8}{2})^2 + 5.66^2} +8\sqrt{(\dfrac{8}{2})^2+ 5.66^2}\\\\ Lateral \ area = 110.89[/tex]
The total surface area of the pyramid will be
Slant height = 8 × sin 60° = 6.93
[tex]\rm T.S.A. = 4(area \ of \ triangle ) + area of base\\\\T.S.A. = 4[\dfrac{1}{2} *8*6.93]+8*8\\\\T.S.A. = 174.88[/tex]
More about the geometry link is given below.
https://brainly.com/question/7558603
