What is the surface area of a rectangular prism whose dimensions are 334 dm×412 dm×5 dm in square decimeters?(1 point)
Responses
16 dm2
16 dm squared
5818 8 dm2
58 Start Fraction 1 over 8 End Fraction dm squared
11614 dm2
116 Start Fraction 1 over 4 End Fraction dm squared
8438 dm2
8438 dm squared
To find the surface area of a rectangular prism, you need to calculate the area of each face and then sum them together.
Given dimensions:
Length (l) = 334 dm
Width (w) = 412 dm
Height (h) = 5 dm
The surface area (SA) can be calculated as follows:
1) SA of the top and bottom faces:
The top and bottom faces are rectangles with dimensions l x w. So, the area of each face is lw.
Area of the top face = 334 dm * 412 dm = 137,608 dm²
Area of the bottom face = 334 dm * 412 dm = 137,608 dm²
Total area of the top and bottom faces = 137,608 dm² + 137,608 dm² = 275,216 dm²
2) SA of the front and back faces:
The front and back faces are rectangles with dimensions l x h. So, the area of each face is lh.
Area of the front face = 334 dm * 5 dm = 1,670 dm²
Area of the back face = 334 dm * 5 dm = 1,670 dm²
Total area of the front and back faces = 1,670 dm² + 1,670 dm² = 3,340 dm²
3) SA of the left and right faces:
The left and right faces are rectangles with dimensions w x h. So, the area of each face is wh.
Area of the left face = 412 dm * 5 dm = 2,060 dm²
Area of the right face = 412 dm * 5 dm = 2,060 dm²
Total area of the left and right faces = 2,060 dm² + 2,060 dm² = 4,120 dm²
Finally, sum up the areas of all the faces to get the total surface area:
Total surface area = Area of top and bottom faces + Area of front and back faces + Area of left and right faces
Total surface area = 275,216 dm² + 3,340 dm² + 4,120 dm²
Total surface area = 282,676 dm²
So, the surface area of the rectangular prism is 282,676 dm².
To find the surface area of a rectangular prism, you need to calculate the area of each of its six faces and then sum them up.
In this case, the rectangular prism has dimensions of 334 dm × 412 dm × 5 dm.
To find the surface area, you need to find the area of the six faces:
1. The top and bottom faces both have dimensions of 334 dm × 412 dm, so their combined area is (334 dm) × (412 dm) = 137 608 dm².
2. The side faces have dimensions of 334 dm × 5 dm, so there are two of them with a combined area of 2 × (334 dm) × (5 dm) = 3340 dm².
3. The other two side faces have dimensions of 412 dm × 5 dm, so there are two of them with a combined area of 2 × (412 dm) × (5 dm) = 4120 dm².
4. Finally, you add up these areas: 137 608 dm² + 3340 dm² + 4120 dm² = 144 068 dm².
Therefore, the surface area of the rectangular prism is 144 068 dm².