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.
What is the surface area of a rectangular prism whose dimensions are 3 3/4dm×4 1/2dm×5dm in square decimeters?
3 answers
7
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