To find the amount of plastic wrap needed to cover the wedge of cheese, we first need to find the surface area of the triangular prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base)(height)
First, we need to calculate the base area of the triangle. We can use the formula for the area of a triangle, which is (1/2)(base)(height).
The base of the triangle is the side of length 13, and the height is 9.
Base area = (1/2)(13)(9) = 58.5
Next, we need to calculate the perimeter of the base. Since the triangle has sides of lengths 9, 5, and 13, the perimeter is 9 + 5 + 13 = 27.
Now we can substitute these values into the formula for the surface area of the triangular prism:
Surface Area = 2(58.5) + (27)(9)
Surface Area = 117 + 243
Surface Area = 360
Therefore, the surface area of the triangular prism (wedge of cheese) is 360 square units. This is the amount of plastic wrap needed to cover the wedge of cheese.
the sides are 9,5, and 13.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
5 answers
the sides are 5,9, and 13.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
To find the amount of plastic wrap needed to cover the wedge of cheese, we first need to find the surface area of the triangular prism.
The formula for the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base)(height)
First, we need to calculate the base area of the triangle. We can use the formula for the area of a triangle, which is (1/2)(base)(height).
The base of the triangle is the side of length 13, and the height is 5.
Base area = (1/2)(13)(5) = 32.5
Next, we need to calculate the perimeter of the base. Since the triangle has sides of lengths 5, 9, and 13, the perimeter is 5 + 9 + 13 = 27.
Now we can substitute these values into the formula for the surface area of the triangular prism:
Surface Area = 2(32.5) + (27)(5)
Surface Area = 65 + 135
Surface Area = 200
Therefore, the surface area of the triangular prism (wedge of cheese) is 200 square units. This is the amount of plastic wrap needed to cover the wedge of cheese.
The formula for the surface area of a triangular prism is:
Surface Area = 2(base area) + (perimeter of base)(height)
First, we need to calculate the base area of the triangle. We can use the formula for the area of a triangle, which is (1/2)(base)(height).
The base of the triangle is the side of length 13, and the height is 5.
Base area = (1/2)(13)(5) = 32.5
Next, we need to calculate the perimeter of the base. Since the triangle has sides of lengths 5, 9, and 13, the perimeter is 5 + 9 + 13 = 27.
Now we can substitute these values into the formula for the surface area of the triangular prism:
Surface Area = 2(32.5) + (27)(5)
Surface Area = 65 + 135
Surface Area = 200
Therefore, the surface area of the triangular prism (wedge of cheese) is 200 square units. This is the amount of plastic wrap needed to cover the wedge of cheese.
the sides are 13,9, and 5.
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
To find the amount of plastic wrap needed to cover the wedge of cheese shaped like a triangular prism with sides 13, 9, and 5, we need to calculate the total surface area of the prism.
First, let's determine the surface area of the triangular base. We will use Heron's formula to calculate the area of the triangle:
Step 1: Calculate the semi-perimeter of the triangle
s = (13 + 9 + 5) / 2 = 13.5
Step 2: Calculate the area of the triangle using Heron's formula
Area = sqrt(13.5 * (13.5 - 13) * (13.5 - 9) * (13.5 - 5))
Area = sqrt(13.5 * 0.5 * 4.5 * 8.5)
Area = sqrt(257.625)
Area ≈ 16.05 (rounded to two decimal places)
Next, we calculate the lateral surface area of the prism. The lateral surface area is the sum of the areas of the three rectangular faces of the prism:
Lateral Surface Area = Perimeter of the base * height
Lateral Surface Area = 27 * 13
Lateral Surface Area = 351
Since the prism has two triangular bases and three rectangular lateral faces, the total surface area is the sum of the area of the two bases and the lateral surface area:
Total Surface Area = 2 * Area of triangular base + Lateral Surface Area
Total Surface Area = 2 * 16.05 + 351
Total Surface Area ≈ 383.1 (rounded to one decimal place)
Therefore, approximately 383.1 square units of plastic wrap are needed to cover the wedge of cheese shaped like a triangular prism with sides 13, 9, and 5.
First, let's determine the surface area of the triangular base. We will use Heron's formula to calculate the area of the triangle:
Step 1: Calculate the semi-perimeter of the triangle
s = (13 + 9 + 5) / 2 = 13.5
Step 2: Calculate the area of the triangle using Heron's formula
Area = sqrt(13.5 * (13.5 - 13) * (13.5 - 9) * (13.5 - 5))
Area = sqrt(13.5 * 0.5 * 4.5 * 8.5)
Area = sqrt(257.625)
Area ≈ 16.05 (rounded to two decimal places)
Next, we calculate the lateral surface area of the prism. The lateral surface area is the sum of the areas of the three rectangular faces of the prism:
Lateral Surface Area = Perimeter of the base * height
Lateral Surface Area = 27 * 13
Lateral Surface Area = 351
Since the prism has two triangular bases and three rectangular lateral faces, the total surface area is the sum of the area of the two bases and the lateral surface area:
Total Surface Area = 2 * Area of triangular base + Lateral Surface Area
Total Surface Area = 2 * 16.05 + 351
Total Surface Area ≈ 383.1 (rounded to one decimal place)
Therefore, approximately 383.1 square units of plastic wrap are needed to cover the wedge of cheese shaped like a triangular prism with sides 13, 9, and 5.