find the surface area of a rectangular prism that is 3 1/2 feet by 4 1/4 feet by 6 feet
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To find the surface area of a rectangular prism, you need to calculate the areas of all six faces and then add them up.
First, let's calculate the areas of the rectangular faces.
1. Face 1: Length x Width
Area = 3 1/2 feet x 4 1/4 feet
= (7/2) feet x (17/4) feet
= (7/2) x (17/4) square feet
= (119/8) square feet
2. Face 2: Length x Width
Area = 3 1/2 feet x 4 1/4 feet
= (7/2) feet x (17/4) feet
= (7/2) x (17/4) square feet
= (119/8) square feet
Now, let's calculate the areas of the square faces.
3. Face 3: Width x Height
Area = 4 1/4 feet x 6 feet
= (17/4) feet x 6 feet
= (17/4) x 6 square feet
= (51/2) square feet
4. Face 4: Width x Height
Area = 4 1/4 feet x 6 feet
= (17/4) feet x 6 feet
= (17/4) x 6 square feet
= (51/2) square feet
Lastly, let's calculate the areas of the remaining two faces.
5. Face 5: Length x Height
Area = 3 1/2 feet x 6 feet
= (7/2) feet x 6 feet
= (7/2) x 6 square feet
= 21 square feet
6. Face 6: Length x Height
Area = 3 1/2 feet x 6 feet
= (7/2) feet x 6 feet
= (7/2) x 6 square feet
= 21 square feet
Now add up the areas of all six faces to calculate the total surface area of the rectangular prism:
Total Surface Area = Face 1 + Face 2 + Face 3 + Face 4 + Face 5 + Face 6
= (119/8) + (119/8) + (51/2) + (51/2) + 21 + 21 square feet
= (238/8) + (102/2) + 42 square feet
= 29.75 + 51 + 42 square feet
= 122.75 square feet
Therefore, the surface area of the given rectangular prism is 122.75 square feet.
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.
The formula to find the surface area of a rectangular prism is:
Surface Area = 2(lw + lh + wh)
Given dimensions:
Length (l) = 3 1/2 feet
Width (w) = 4 1/4 feet
Height (h) = 6 feet
Let's start by finding the area of each face, and then we will add them together.
1. Top and bottom faces:
The top and bottom faces are both rectangles with dimensions l (length) and w (width).
Area of each top/bottom face = lw
2. Front and back faces:
The front and back faces are also rectangles, but with dimensions l (length) and h (height).
Area of each front/back face = lh
3. Left and right side faces:
The left and right side faces are the last two rectangles, with dimensions w (width) and h (height).
Area of each left/right side face = wh
Now, let's substitute the given dimensions into the formula and calculate the surface area:
1. Top/bottom faces: Area = lw
Area of the top/bottom faces = (3 1/2 feet) * (4 1/4 feet)
2. Front/back faces: Area = lh
Area of the front/back faces = (3 1/2 feet) * (6 feet)
3. Left/right side faces: Area = wh
Area of the left/right side faces = (4 1/4 feet) * (6 feet)
Finally, let's calculate the surface area by adding up the areas of all six faces:
Surface Area = 2(lw + lh + wh)
Surface Area = 2((3 1/2)*(4 1/4) + (3 1/2)*(6) + (4 1/4)*(6))
To get the final answer, perform the calculations using the appropriate method, whether manually or using a calculator.