To find the total surface area of Kym's sawhorse, we will calculate the surface area of each of its sides and then sum them up. The sawhorse can be thought of as a box (with two triangular ends) plus the top surface.
The dimensions given are:
- Height (h) = 39 inches
- Length (l) = 27 inches
- Width (w) = 19 inches
Step 1: Calculate the surface area of the rectangular sides
We have two types of rectangular sides:
- Two sides of length (l) and height (h)
- Two sides of width (w) and height (h)
- One side on top with length (l) and width (w)
Areas of the rectangular sides:
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The area of the two sides (length x height): \[ \text{Area}_{side1} = 2 \times (l \times h) = 2 \times (27 \times 39) = 2 \times 1053 = 2106 \text{ square inches} \]
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The area of the two sides (width x height): \[ \text{Area}_{side2} = 2 \times (w \times h) = 2 \times (19 \times 39) = 2 \times 741 = 1482 \text{ square inches} \]
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The area of the top (length x width): \[ \text{Area}_{top} = l \times w = 27 \times 19 = 513 \text{ square inches} \]
Step 2: Calculate the total surface area
Now, add all the areas together: \[ \text{Total Surface Area} = \text{Area}{side1} + \text{Area}{side2} + \text{Area}_{top} \] \[ \text{Total Surface Area} = 2106 + 1482 + 513 = 4101 \text{ square inches} \]
Thus, the total surface area of Kym's sawhorse is: \[ \boxed{4101.00} \text{ square inches} \]