Question

A wedge of cheese is shaped like a triangular prism how much plastic wrap is needed to cover the wedge of cheese if the base is 12 cm, the height is 5 cm, the length is 9 cm, and the slant is 13 cm

Answer 1

To calculate the amount of plastic wrap needed to cover the wedge of cheese, we need to find the total surface area of the triangular prism.

The total surface area of a triangular prism can be calculated by finding the area of the two triangular bases and the area of the three rectangular faces.

1. Area of the two triangular bases:
- Base = 12 cm
- Height = 5 cm
- Area = 1/2 x base x height
= 1/2 x 12 x 5
= 30 cm²

Since there are two triangular bases, the total area of the two triangular bases is 2 x 30 cm² = 60 cm².

2. Area of the three rectangular faces:
- Length = 9 cm
- Slant height = 13 cm
- Height = 5 cm
- Area = perimeter x height
= 2(length + slant height) x height
= 2(9 + 13) x 5
= 2(22) x 5
= 2 x 22 x 5
= 220 cm²

Since there are three rectangular faces, the total area of the three rectangular faces is 3 x 220 cm² = 660 cm².

Therefore, the total surface area of the triangular prism is 60 cm² (two triangular bases) + 660 cm² (three rectangular faces) = 720 cm².

To cover the wedge of cheese with plastic wrap, we would need 720 cm² of plastic wrap.