Answer:
x= 4 inches
Step-by-step explanation:
Surface Area Of A Square Pyramid
It can be computed by adding the area of the base plus 4 times the area of the sides. The area of the base (a square) is
[tex]\displaystyle A_b=L^2=36\ in^2[/tex]
The area of each lateral side (a triangle) is
[tex]\displaystyle A_s=\frac{1}{2}LX=\frac{1}{2}(6)x=3X[/tex]
The total area of the pyramid is
[tex]\displaystyle A_b+4A_S[/tex]
It must be equal to 84, so
[tex]\displaystyle 36+4(3X)=84[/tex]
[tex]\displaystyle 12X=48[/tex]
Solving for x
[tex]\boxed{\displaystyle X=4\ in}[/tex]
