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

Answer 1

To find the total surface area of the sawhorse, we first need to find the area of each of its four sides and its top.

1. Area of the top:
Since the top of the sawhorse is a rectangle, its area is length multiplied by width.
Area of top = 27 inches x 19 inches = 513 square inches

2. Area of the four sides:
We can divide the sawhorse into two right triangles and a rectangle. Since the hypotenuse (diagonal) is given, we can use the Pythagorean theorem to find the height of the triangles.
a^2 + b^2 = c^2
27^2 + 19^2 = c^2
729 + 361 = c^2
1090 = c^2
c ≈ 33 inches

Now we have the height of the triangles, we can calculate the area of each triangle and the side rectangle.

Area of side triangle = 0.5 x base x height
Area of side triangles = 0.5 x 27 inches x 33 inches = 445.5 square inches (for each triangle)
Area of side rectangle = length x height
Area of side rectangle = 27 inches x 33 inches = 891 square inches (for both rectangles)

3. Total surface area:
Total surface area = 2 x (area of top) + 2 x (area of side triangle) + (area of side rectangle)
Total surface area = 2(513) + 2(445.5) + 891
Total surface area = 1026 + 891 + 891
Total surface area = 2808 square inches

Therefore, the total surface area of Kym's sawhorse is 2808 square inches.