What is the surface area of the rectangular prism that has side lengths of 3 mm, 5 mm, and 4 mm?
The surface area of the rectangular prism is 94 mm².
2(3*5) + 2(4*5) + 2(3*4)
= 30 + 40 + 24
= 94
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To find the surface area of a rectangular prism, we need to calculate the area of each of its sides and then sum them up.
A rectangular prism has six sides: a bottom face, a top face, a front face, a back face, a left face, and a right face.
The formula to find the surface area of a rectangular prism is given by:
Surface Area = 2lw + 2lh + 2wh
where l is the length, w is the width, and h is the height of the rectangular prism.
Given the side lengths: l = 3 mm, w = 5 mm, and h = 4 mm, we can substitute these values into the formula:
Surface Area = 2(3 * 5) + 2(3 * 4) + 2(5 * 4)
Surface Area = 30 + 24 + 40
Surface Area = 94 mm²
Therefore, the surface area of the rectangular prism with side lengths of 3 mm, 5 mm, and 4 mm is 94 mm².
To find the surface area of a rectangular prism, you need to calculate the area of each face and then add them up. A rectangular prism has six faces: two identical rectangular bases and four rectangular side faces.
In this case, the side lengths are given as 3 mm, 5 mm, and 4 mm. To calculate the surface area, follow these steps:
1. Calculate the area of one of the bases:
- The base is a rectangle, so its area is given by multiplying the length and width.
- In this case, the length is 3 mm and the width is 5 mm.
- Therefore, the area of one base is 3 mm x 5 mm = 15 mm².
2. Multiply the area of the base by 2 since there are two identical bases:
- 15 mm² * 2 = 30 mm².
3. Calculate the area of each of the four side faces:
- Two sides have dimensions 3 mm x 4 mm.
- The other two sides have dimensions 5 mm x 4 mm.
4. Calculate the area of each side face:
- For the first two sides: 3 mm x 4 mm = 12 mm².
- For the other two sides: 5 mm x 4 mm = 20 mm².
5. Add up the areas of all six faces to get the total surface area:
- Total surface area = 2 * 15 mm² + 2 * 12 mm² + 2 * 20 mm² = 30 mm² + 24 mm² + 40 mm² = 94 mm².
So, the surface area of the rectangular prism with side lengths of 3 mm, 5 mm, and 4 mm is 94 mm².