Use the image to answer the question.
An illustration shows a rectangular prism with length 10 inches, width 9 inches, and height 3 inches. The top, front, and right faces are visible. The edges that are not visible are represented by dashed lines.
What is the surface area of the rectangular prism?
The surface area of the rectangular prism can be found by adding up the areas of all six faces. The visible faces are the top, front, and right faces, each with an area of length times width. So the surface area is:
2(length x width) + 2(width x height) + 2(length x height)
= 2(10 x 9) + 2(9 x 3) + 2(10 x 3)
= 180 + 54 + 60
= 294 square inches
Therefore, the surface area of the rectangular prism is 294 square inches.
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To find the surface area of the rectangular prism, we need to calculate the areas of all its faces and add them together.
The rectangular prism has six faces: the top, bottom, front, back, left, and right faces.
Let's calculate the areas of each face:
1. The top face has a length of 10 inches and a width of 9 inches, so its area is 10 inches x 9 inches = 90 square inches.
2. The bottom face has the same dimensions as the top face, so its area is also 90 square inches.
3. The front face has a height of 3 inches and a width of 9 inches, so its area is 3 inches x 9 inches = 27 square inches.
4. The back face has the same dimensions as the front face, so its area is also 27 square inches.
5. The left face has a length of 10 inches and a height of 3 inches, so its area is 10 inches x 3 inches = 30 square inches.
6. The right face has the same dimensions as the left face, so its area is also 30 square inches.
Now, let's add up the areas of all the faces:
90 square inches (top) + 90 square inches (bottom) + 27 square inches (front) + 27 square inches (back) + 30 square inches (left) + 30 square inches (right) = 294 square inches.
Therefore, the surface area of the rectangular prism is 294 square inches.