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 point)
The surface area of a rectangular prism (which a sawhorse resembles) can be found using the formula: 2lw + 2lh + 2wh, where l, w, and h are the length, width, and height, respectively.
So, for Kym's sawhorse:
- l = 27 inches
- w = 19 inches
- h = 39 inches
Substituting these values into the formula:
2(27)(19) + 2(27)(39) + 2(19)(39) = 1,494 square inches
Therefore, the total surface area of Kym's sawhorse is 1,494 square inches, rounded to the nearest hundredth.
To find the total surface area of a cuboid or rectangular prism, we need to calculate the sum of the areas of all its faces.
The total surface area can be determined by adding the areas of the six faces:
1. Top and bottom faces: The top and bottom faces are both rectangles and have the same dimensions. The area of each face is its length multiplied by its width. So, for each of these faces, the area is 27 inches × 19 inches = 513 square inches.
2. Side faces: Each side face is a rectangle. The area of each side face is its height multiplied by its width. So, for each of these faces, the area is 39 inches × 19 inches = 741 square inches.
3. Front and back faces: Each front and back face is a rectangle. The area of each face is its length multiplied by its height. So, for each of these faces, the area is 27 inches × 39 inches = 1053 square inches.
To find the total surface area, we add up all the areas:
513 square inches (top face) + 513 square inches (bottom face) + 741 square inches (side face 1) + 741 square inches (side face 2) + 1053 square inches (front face) + 1053 square inches (back face) = 4614 square inches.
So, the total surface area of Kym's sawhorse is 4614 square inches (rounded to the nearest hundredth).