Answer:
[tex]Area= 84 \ in^2[/tex]
Step-by-step explanation:
The surface area of a pyramid is equivalent to the area of its base plus area of it's 4 triangles.
#The pyramid has a square base with lengths equal to the triangle's base length:
[tex]A=s\times s=s^2\\\\=6^2\\\\=36\ in^2[/tex]
#The area of the side triangles is calculated as:
[tex]A=0.5bh\\\\=0.5\times 6\times 4\\\\=12\\\\\therefore A_t=4A=12\times 4=48\ in^2[/tex]
We sum the two area to find the net surface area of the pyramid:
[tex]A=A_b+A_t\\\\=36+48\\\\=84\ in^2[/tex]
Hence, the pyramid's surface area is [tex]84 \ in^2[/tex]
