Answer:
The total surface area is 117.2 square inches.
Explanation:
The surface area of a rectangular pyramid is formed by one rectangle at the center, and four triangles attached to it.
In this case, the rectangle has dimensions of 10 inches (height) by 4 inches (length). 2 triangles have a base of 10 inches and a height of 5 inches. The other 2 triangles have a an area of 13.6 square inches.
Basically, we need to find the area of the other two triangles and the area of the rectangle at the center.
Area of the rectangle.
![A_(1)=4 * 10 = 40 \ in^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/5ki0rcy9csfasja1ugr2har4xqgsg9x416.png)
Area of the missing triangles.
![A_(2)= 2((1)/(2) * 10 * 5 )=2(25) \ in^(2) = 50 \ in^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/92173kkye2tlajadnxjhznhakczzixrm9r.png)
Now, we sum all areas
![A=40 + 50 + 13.6 +13.6= 117.2 \ in^(2)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/j9azb186wa8u2eqi1x8cgrekmtd6jxyhoh.png)
Therefore, the total surface area is 117.2 square inches.