Determine the minimum amount of packaging needed to completely cover a triangular prism toblerone bar with these dimensions: length 22.5cm; triangular face gas edges 4.5cm and height 4.0cm. Express the surface area to the nearest square centimeter.
Thanks so much steve
has not gas
area of triangular base: 1/2 (4.5)(4) = 9
area of lateral (rectangular) face: 22.5*4.5 = 101.25
total area = 2 bases + 3 faces = 2*9 + 3*101.25 = 321.75
the answer to the problem is 408 square inches
To determine the minimum amount of packaging needed to completely cover a triangular prism Toblerone bar, we need to calculate the surface area of the prism. The surface area accounts for all the sides that need to be covered.
A triangular prism consists of two triangular faces and three rectangular faces. Let's calculate the surface area step by step:
1. Triangular Faces: The base of the Toblerone bar is a triangle. The triangular face has a base length of 4.5 cm and a height of 4.0 cm. To calculate the area of a triangle, we use the formula: Area = (base * height) / 2. So, the area of one triangular face is:
Area of one triangular face = (4.5 cm * 4.0 cm) / 2 = 18 cm²
Since there are two triangular faces, we double the area to account for both, resulting in a total area of:
Total area of triangular faces = 2 * 18 cm² = 36 cm²
2. Rectangular Faces: A triangular prism has three rectangular faces. The dimensions of these faces depend on the length and height of the prism.
The length of the prism is given as 22.5 cm. The height of the prism is 4.0 cm. The width of each rectangular face is the height of the triangular face, which is 4.0 cm. To calculate the area of a rectangle, we use the formula: Area = length * width.
Area of one rectangular face = length * height = 22.5 cm * 4.0 cm = 90 cm²
Since there are three rectangular faces, we triple the area to account for all of them, resulting in a total area of:
Total area of rectangular faces = 3 * 90 cm² = 270 cm²
3. Total Surface Area: To find the total surface area, we sum up the areas of the triangular faces and the rectangular faces.
Total surface area = Total area of triangular faces + Total area of rectangular faces
Total surface area = 36 cm² + 270 cm² = 306 cm²
Therefore, the minimum amount of packaging needed to completely cover the Toblerone bar is 306 square centimeters.