Question 1043884
.
a square pyramid has a height of 1.5 inches, a slant height of 3.9 inches and a volume of 25.92 inches cubed. 
to the nearest square inch, what is the lateral surface area of the pyramid?
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<pre>
1.  Divide the volume of the pyramid by the height and multiply by 3.
    You will get the area of the base:

    A = {{{(25.92*3)/1.5}}} = 51.84 square inches.


2.  Take the square root of the area of the base to get the length of the edge at the base 

    {{{sqrt(A)}}} = {{{sqrt(51.84)}}} = 7.2 inches.


3.  Calculate the area of one lateral face, which is a triangle:

    S = {{{(1/2)*7.2*3.9}}} = 14.04 square inches.


4.  Multiply it by 4 to get the full lateral surface, consisting of 4 faces:

    4*14.04 = 56.16 square inches.


5.  It is your answer.
</pre>

On surface area of pyramids see the lessons

&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>

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/OVERVIEW-of-LESSONS-on-surface-area-of-pyramids.lesson>Overview of lessons on surface area of pyramids</A>

in this site.


Moreover, you have free of charge online textbook in 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.