Kym’s sawhorse is 39 inches

tall, 27 inches long, and 19
inches wide. Its 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 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:

  1. Two sides of length (l) and height (h)
  2. Two sides of width (w) and height (h)
  3. One side on top with length (l) and width (w)

Areas of the rectangular sides:

  1. The area of the two sides (length x height): \[ \text{Area}_{side1} = 2 \times (l \times h) = 2 \times (27 \times 39) = 2 \times 1053 = 2106 \text{ square inches} \]

  2. The area of the two sides (width x height): \[ \text{Area}_{side2} = 2 \times (w \times h) = 2 \times (19 \times 39) = 2 \times 741 = 1482 \text{ square inches} \]

  3. 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: \[ \boxed{4101.00} \text{ square inches} \]