What is the surface area of a rectangular prism measuring 3 1/2 ft.by 2 3/8 ft. by 8 feet ?
What don't you understand about how to solve this problem?
To find the surface area of a rectangular prism, you need to calculate the area of each face and then add up those areas.
A rectangular prism has six faces: front, back, top, bottom, left side, and right side.
1. First, calculate the area of the front and back faces. Use the formula: length × width.
- For the front face: 3 1/2 ft × 8 ft = 28 ft²
- For the back face: 3 1/2 ft × 8 ft = 28 ft²
2. Next, calculate the area of the top and bottom faces. Again, use the formula: length × width.
- For the top face: 2 3/8 ft × 8 ft = 19 ft²
- For the bottom face: 2 3/8 ft × 8 ft = 19 ft²
3. Finally, calculate the area of the left and right side faces. Apply the same formula: length × width.
- For the left side face: 3 1/2 ft × 2 3/8 ft = 8 3/8 ft²
- For the right side face: 3 1/2 ft × 2 3/8 ft = 8 3/8 ft²
4. Now, add up the areas of all the faces to find the total surface area of the rectangular prism.
- Total surface area = Front + Back + Top + Bottom + Left side + Right side
- Total surface area = 28 ft² + 28 ft² + 19 ft² + 19 ft² + 8 3/8 ft² + 8 3/8 ft²
To simplify, convert the mixed fraction to an improper fraction:
- 8 3/8 ft² = (8 × 8 + 3) / 8 ft² = 67/8 ft²
Add the areas together:
- Total surface area = 28 ft² + 28 ft² + 19 ft² + 19 ft² + 67/8 ft² + 67/8 ft²
To add the fractions, find a common denominator:
- 67/8 ft² + 67/8 ft² = (67 + 67) / 8 ft² = 134/8 ft² = 67/4 ft²
Now, simplify the fraction:
- 67/4 ft² = 16 3/4 ft²
Therefore, the surface area of the given rectangular prism is 16 3/4 square feet.