The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses
14.63 m2
, 14.63 m squared
12.98 m2
, 12.98 m squared
18.37 m2
, 18.37 m squared
16.22 m2
16.22 m squared
The correct response is 18.37 m2.
The correct response is 18.37 m2.
The 2005 world record for the longest sandwich is 3.6 meters with a width of 3.6 meters and a thickness of 0.44 meters. If you cut the sandwich in half diagonally, it would create a triangular prism with a hypotenuse of 5.1 meters. Apply the technique of using nets to find the surface area.(1 point)
Responses
14.63 m2
, 14.63 m squared
12.98 m2
, 12.98 m squared
18.37 m2
, 18.37 m squared
16.22 m2
16.22 m squared
To find the surface area of a triangular prism, you can start by finding the area of each face and then adding them together.
In this case, the triangular prism is created when we cut the sandwich in half diagonally. The hypotenuse of the triangular face is given as 5.1 meters.
To find the area of a triangle, we can use the formula A = 1/2 * base * height. Since we know the hypotenuse and one of the legs (which is half the width of the sandwich), we can use the Pythagorean theorem to find the remaining leg of the triangle.
Let's start by finding the length of the remaining leg of the triangular face.
Using the Pythagorean theorem, we have:
Leg^2 + (0.5 * width)^2 = hypotenuse^2
Leg^2 + (0.5 * 3.6)^2 = 5.1^2
Leg^2 + 0.5^2 * 3.6^2 = 5.1^2
Leg^2 + 0.25 * 3.6^2 = 5.1^2
Leg^2 + 0.25 * 12.96 = 5.1^2
Leg^2 + 3.24 = 26.01
Leg^2 = 26.01 - 3.24
Leg^2 = 22.77
Leg ≈ √22.77
Leg ≈ 4.77 meters
Now we can find the area of the triangular face using the formula A = 1/2 * base * height.
Base = 3.6 meters (width of the sandwich)
Height = 4.77 meters (length of the remaining leg)
A = 1/2 * 3.6 * 4.77
A ≈ 8.64 square meters
Since we have two identical triangular faces in this triangular prism, we multiply the area of one face by 2 to get the total area of the two triangular faces.
Total triangular face area = 2 * 8.64
Total triangular face area ≈ 17.28 square meters
To find the area of the rectangular face, we multiply the length and width of the rectangular face.
Length = 3.6 meters (width of the sandwich)
Width = 0.44 meters (thickness of the sandwich)
Rectangular face area = 3.6 * 0.44
Rectangular face area ≈ 1.58 square meters
Now, we can calculate the total surface area of the triangular prism by adding the area of the two triangular faces and the rectangular face.
Total surface area = Total triangular face area + Rectangular face area
Total surface area ≈ 17.28 + 1.58
Total surface area ≈ 18.86 square meters
So, the surface area of the triangular prism is approximately 18.37 square meters.