To find the total surface area of Kim's sawhorse, we will calculate the surface area of the rectangular prism that the sawhorse forms. Since the sawhorse is a three-dimensional shape, we need to find the area of all its surfaces.
Given the dimensions:
- Height (h) = 39 inches
- Length (l) = 27 inches
- Width (w) = 19 inches
The total surface area (SA) of a rectangular prism can be calculated using the formula:
\[ SA = 2(lw + lh + wh) \]
Now we can substitute in the values:
-
Calculate \(lw\): \[ lw = 27 \times 19 = 513 \]
-
Calculate \(lh\): \[ lh = 27 \times 39 = 1053 \]
-
Calculate \(wh\): \[ wh = 19 \times 39 = 741 \]
Now we can add these areas together: \[ lw + lh + wh = 513 + 1053 + 741 = 2307 \]
Finally, multiply by 2 to find the total surface area: \[ SA = 2 \times 2307 = 4614 \]
Thus, the total surface area of Kim's sawhorse is:
\[ \boxed{4614} \text{ square inches} \]