Answer:
![Area= 84 \ in^2](https://img.qammunity.org/2021/formulas/mathematics/college/oie0ypz5o079fjrowzvnnwc0qzshrbkftu.png)
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:
![A=s* s=s^2\\\\=6^2\\\\=36\ in^2](https://img.qammunity.org/2021/formulas/mathematics/college/jjjyv5waqu7fxgcawh0je9nzvb65c2kydu.png)
#The area of the side triangles is calculated as:
![A=0.5bh\\\\=0.5* 6* 4\\\\=12\\\\\therefore A_t=4A=12* 4=48\ in^2](https://img.qammunity.org/2021/formulas/mathematics/college/h2is0awy0ydz3u27xk6a7ny09ld147bqqw.png)
We sum the two area to find the net surface area of the pyramid:
![A=A_b+A_t\\\\=36+48\\\\=84\ in^2](https://img.qammunity.org/2021/formulas/mathematics/college/isztdlbs88qemwg0jispen0cug345ieio7.png)
Hence, the pyramid's surface area is
![84 \ in^2](https://img.qammunity.org/2021/formulas/mathematics/college/a0qup35yfwdgrukfxket8lghkix1svre0n.png)