What is the surface area of a rectangular prism whose dimensions are 3 3/4dm×4 1/2dm×5dm in square decimeters?
To find the surface area of a rectangular prism, we need to add up the areas of all six faces. Each face has a length times width dimension, so we multiply the dimensions in pairs to find the area of each face.
The six faces of the rectangular prism are:
1. Top face: 3 3/4 dm × 4 1/2 dm = (15/4) dm × (9/2) dm = 67.5/8 dm²
2. Bottom face: 3 3/4 dm × 4 1/2 dm = 67.5/8 dm²
3. Front face: 3 3/4 dm × 5 dm = 15/4 dm × 20/4 dm = 75/4 dm²
4. Back face: 3 3/4 dm × 5 dm = 75/4 dm²
5. Left side face: 4 1/2 dm × 5 dm = 9/2 dm × 20/4 dm = 45/2 dm²
6. Right side face: 4 1/2 dm × 5 dm = 45/2 dm²
To find the total surface area, we add up all six face areas:
67.5/8 dm² + 67.5/8 dm² + 75/4 dm² + 75/4 dm² + 45/2 dm² + 45/2 dm²
= 135/4 dm² + 150/4 dm² + 45/2 dm²
= 225/2 dm²
= 112.5 dm²
Therefore, the surface area of the rectangular prism is 112.5 square decimeters.
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I'm sorry, I'm not sure what you are asking for. Can you please provide more context or information?
To find the surface area of a rectangular prism, you need to find the area of each face and then add them up.
First, let's convert the dimensions of the rectangular prism into decimals:
Length = 3 3/4 dm = 3.75 dm
Width = 4 1/2 dm = 4.5 dm
Height = 5 dm
Now, let's calculate the area of each face:
1. Front and back faces: Length × Height = 3.75 dm × 5 dm = 18.75 dm² (each face has the same area)
2. Top and bottom faces: Width × Height = 4.5 dm × 5 dm = 22.5 dm² (each face has the same area)
3. Side faces: Length × Width = 3.75 dm × 4.5 dm = 16.875 dm² (each face has the same area)
To find the total surface area, add up the areas of all the faces:
18.75 dm² (front) + 18.75 dm² (back) + 22.5 dm² (top) + 22.5 dm² (bottom) + 16.875 dm² (side 1) + 16.875 dm² (side 2) = 116.25 dm²
Therefore, the surface area of the rectangular prism is 116.25 square decimeters.