Kim's sawhorse is 39 inches tall, 27 inches long, and 19 inches wide. It's diagonal measurement, or the hypotenuse, is 40.14 inches. What is its total surface area? Round your answer to the nearest hundredth.

1 answer

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:

  1. Calculate \(lw\): \[ lw = 27 \times 19 = 513 \]

  2. Calculate \(lh\): \[ lh = 27 \times 39 = 1053 \]

  3. 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:

\[ \boxed{4614} \text{ square inches} \]