Answer :
To find the surface area of a rectangular prism, we can consider the three different types of faces that make up the prism:
1. The two faces that are width by height (W x H)
2. The two faces that are length by height (L x H)
3. The two faces that are length by width (L x W)
The surface area is the sum of the areas of all six faces. Since we have two of each type, the surface area (SA) equation is:
SA = 2(LW) + 2(LH) + 2(WH)
Now, let's plug in the given dimensions of the rectangular prism:
Length (L) = 2 feet
Width (W) = 3 feet
Height (H) = 4 feet
SA = 2(2 feet 3 feet) + 2(2 feet 4 feet) + 2(3 feet 4 feet)
Then we calculate the area of each pair of faces:
- The area of the two length by width faces:
2(2 feet 3 feet) = 2 6 square feet = 12 square feet
- The area of the two length by height faces:
2(2 feet 4 feet) = 2 8 square feet = 16 square feet
- The area of the two width by height faces:
2(3 feet 4 feet) = 2 * 12 square feet = 24 square feet
Now, we add up these areas to get the total surface area:
SA = 12 square feet + 16 square feet + 24 square feet
SA = 52 square feet
So, the surface area of the rectangular prism is 52 square feet.
Regarding drawing a net for the rectangular prism:
A net of a 3D object like a rectangular prism is a 2D representation that shows all the faces of the object unfolded. For the given rectangular prism, the net would consist of six rectangles: two of each pair that correspond to the dimensions given (LxW, LxH, and WxH). Unfortunately, I cannot physically draw a net for you here, but imagine a central cross-like shape made of rectangles where the central rectangle would be the base (WxH), and the rectangles sticking out from each side of it would represent the faces LxW and LxH.
Each rectangle's dimensions would be as follows:
- Two rectangles of 3 feet by 4 feet (WxH)
- Two rectangles of 2 feet by 3 feet (LxW)
- Two rectangles of 2 feet by 4 feet (LxH)
1. The two faces that are width by height (W x H)
2. The two faces that are length by height (L x H)
3. The two faces that are length by width (L x W)
The surface area is the sum of the areas of all six faces. Since we have two of each type, the surface area (SA) equation is:
SA = 2(LW) + 2(LH) + 2(WH)
Now, let's plug in the given dimensions of the rectangular prism:
Length (L) = 2 feet
Width (W) = 3 feet
Height (H) = 4 feet
SA = 2(2 feet 3 feet) + 2(2 feet 4 feet) + 2(3 feet 4 feet)
Then we calculate the area of each pair of faces:
- The area of the two length by width faces:
2(2 feet 3 feet) = 2 6 square feet = 12 square feet
- The area of the two length by height faces:
2(2 feet 4 feet) = 2 8 square feet = 16 square feet
- The area of the two width by height faces:
2(3 feet 4 feet) = 2 * 12 square feet = 24 square feet
Now, we add up these areas to get the total surface area:
SA = 12 square feet + 16 square feet + 24 square feet
SA = 52 square feet
So, the surface area of the rectangular prism is 52 square feet.
Regarding drawing a net for the rectangular prism:
A net of a 3D object like a rectangular prism is a 2D representation that shows all the faces of the object unfolded. For the given rectangular prism, the net would consist of six rectangles: two of each pair that correspond to the dimensions given (LxW, LxH, and WxH). Unfortunately, I cannot physically draw a net for you here, but imagine a central cross-like shape made of rectangles where the central rectangle would be the base (WxH), and the rectangles sticking out from each side of it would represent the faces LxW and LxH.
Each rectangle's dimensions would be as follows:
- Two rectangles of 3 feet by 4 feet (WxH)
- Two rectangles of 2 feet by 3 feet (LxW)
- Two rectangles of 2 feet by 4 feet (LxH)
