Use the image to answer the question.
An illustration shows the unfolded version of a rectangular prism composed of 6 rectangles. There are four adjoining rectangles positioned horizontally. The first and third are similar and smaller. The second and fourth are similar and bigger. The first rectangle is labeled 3 meters on the left side vertically and 1.5 meters on the top horizontally. The second rectangle is labeled as 4 meters on the bottom. The fourth rectangle shares the top and bottom sides with two similar rectangles, one on each side.
What is the surface area of the rectangular prism?
Without the exact dimensions of the third and fifth rectangles, we cannot accurately determine the surface area of the rectangular prism.
To find the surface area of the rectangular prism, we need to calculate the area of each of its six faces and then add them together.
1. The top face: The first rectangle has dimensions of 3 meters by 1.5 meters, so its area is 3 * 1.5 = 4.5 square meters.
2. The bottom face: The second rectangle has a dimension of 4 meters by 1.5 meters, so its area is 4 * 1.5 = 6 square meters.
3. The front face: The third rectangle is similar to the first one, so its dimensions are also 3 meters by 1.5 meters, giving us an area of 3 * 1.5 = 4.5 square meters.
4. The back face: Since the fourth rectangle shares its top and bottom sides with two similar rectangles, each with dimensions of 3 meters by 1.5 meters, its area is 3 * 1.5 + 3 * 1.5 = 9 square meters.
5. The left face: The side face is also made up of the fourth rectangle with dimensions of 3 meters by 1.5 meters, so its area is 3 * 1.5 = 4.5 square meters.
6. The right face: This is also a side face and has the same dimensions as the left face, resulting in an area of 4.5 square meters.
To find the total surface area, we add up the areas of all the faces:
4.5 + 6 + 4.5 + 9 + 4.5 + 4.5 = 33 square meters.
Therefore, the surface area of the rectangular prism is 33 square meters.
To find the surface area of the rectangular prism, we need to calculate the area of each rectangle and sum them up.
Let's break down the given information:
- The first rectangle has a height of 3 meters and a width of 1.5 meters. So its area is 3 × 1.5 = 4.5 square meters.
- The second rectangle has a height of 4 meters and a width of 1.5 meters. So its area is 4 × 1.5 = 6 square meters.
- The fourth rectangle shares its top and bottom sides with two similar rectangles, implying that the top and bottom sides have the same length. Since the second rectangle's bottom side is labeled as 4 meters, the fourth rectangle's top side is also 4 meters. Additionally, the fourth rectangle's height is 3 meters. So its area is 4 × 3 = 12 square meters.
Now, we have three rectangles:
1. Area of the first rectangle = 4.5 square meters
2. Area of the second rectangle = 6 square meters
3. Area of the fourth rectangle = 12 square meters
To find the total surface area of the prism, we add up these areas:
4.5 + 6 + 12 = 22.5 square meters
Therefore, the surface area of the rectangular prism is 22.5 square meters.