<u>Given</u>:
Given that the rectangular prism with length l = 2..6 yards.
The width of the rectangular prism is 3.5 yards.
The height of the prism is h yards.
We need to determine the simplified expression for the surface area of the rectangular prism.
We also need to determine the surface area of the prism if the height is 4 yards.
<u>Expression for the surface area of the prism:</u>
The surface area of the rectangular prism can be determined using the formula,
![SA=2(lw+wh+lh)](https://tex.z-dn.net/?f=SA%3D2%28lw%2Bwh%2Blh%29)
Substituting l = 2.6, w = 3.5, h = h, we get;
![SA=2[(2.6)(3.5)+(3.5)h+(2.6)h]](https://tex.z-dn.net/?f=SA%3D2%5B%282.6%29%283.5%29%2B%283.5%29h%2B%282.6%29h%5D)
![SA=2(9.1+3.5h+2.6h)](https://tex.z-dn.net/?f=SA%3D2%289.1%2B3.5h%2B2.6h%29)
![SA=2(9.1+6.1 h)](https://tex.z-dn.net/?f=SA%3D2%289.1%2B6.1%20h%29)
![SA=18.2+12.2h](https://tex.z-dn.net/?f=SA%3D18.2%2B12.2h)
Thus, the simplified expression for the surface area of the prism is ![SA=18.2+12.2h](https://tex.z-dn.net/?f=SA%3D18.2%2B12.2h)
<u>Surface area of the prism:</u>
Now, we shall determine the surface area of the prism if the height is 4 yards.
Substituting the value h = 4 in the expression
, we have;
![SA=18.2+12.2(4)](https://tex.z-dn.net/?f=SA%3D18.2%2B12.2%284%29)
![SA=18.2+48.8](https://tex.z-dn.net/?f=SA%3D18.2%2B48.8)
![SA=67 \ yd^2](https://tex.z-dn.net/?f=SA%3D67%20%5C%20yd%5E2)
Thus, the surface area of the rectangular prism is 67 square yards.