A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?
Responses
287 cm2
287 cm2
- no response given
240 cm2
240 cm2
- no response given
330 cm2
330 cm2
- no response given
810 cm2
To calculate the surface area of the triangular prism (wedge of cheese), we need to find the area of all the faces.
1. Two triangular faces:
Area of one triangle = 1/2 * base * height
Given that both the base and height of the triangle are equal to 12 cm, the area of one triangle is:
1/2 * 12 cm * 12 cm = 72 cm2
Therefore, the total area of both triangular faces is:
2 * 72 cm2 = 144 cm2
2. Three rectangular faces:
Area of one rectangle = length * width
Given that the length is 12 cm and the width is 16 cm, the area of one rectangle is:
12 cm * 16 cm = 192 cm2
Since there are three rectangular faces, the total area of all three is:
3 * 192 cm2 = 576 cm2
Therefore, the total surface area of the triangular prism (wedge of cheese) is:
144 cm2 (triangular faces) + 576 cm2 (rectangular faces) = 720 cm2
So, the answer is 720 cm2, which is not one of the response options provided.