Question 1065774
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The volume of a pyramid is 48 cubic feet. What is its total surface area if the pyramids height is 4 feet and the base is a square? 
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<pre>
the base is a square, four identical sides. The area is s^2

Volume of the pyramid:

{{{(1/3)*s^2*4}}} = 48  --->

4s^2 = 3*48

s^2 = (3*48)/4

s^2 = 36  --->  s = sqrt(36)  ---->  s = 6 feet


Each side of the pyramid is a triangle.

Lateral height of the pyramid is the height of the lateral side.

{{{H^2}}} + {{{(s/2)^2}}} = {{{H[lateral]^2}}}  --->

{{{H[lateral]^2}}} = {{{4^2 + 3^2}}} = {{{25}}}  ---->  {{{H[lateral]}}} = 5 inches.


Area of each lateral side is {{{b*H[lateral]/2}}} = (6*5)/2 = 15 square feet. This is one side.

Our pyramid has four sides:
4*15 = 60 square feet. It is the surface area of four lateral sides.


The base area = s^2 = 6^2 = 36

Total area, four sides plus base:

36 + 60 = 96 square feet. It is the total area of the pyramid.
</pre>

SOLVED.



Lessons on surface area of pyramids in this site:


&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-pyramids.lesson>Surface area of pyramids</A>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-pyramids.lesson>Solved problems on surface area of pyramids</A>


Also, &nbsp;you have this free of charge online textbook on Geometry

&nbsp;&nbsp;&nbsp;&nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A> 

in this site.


The referred lessons are the part if this textbook under the topic "<U>Surface area of 3D solid bodies</U>".



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Dear tutor "addingup".


You demonstrated very low level of knowledge on the subject working on this solution.


I am very disappointed.