13 cm 9 cm 5 cm 12 cm A wedge of cheese is shaped like a trangular prism How much plastic wrap is neoded to cover the wedge of cheese 330 cm 240 cm³ 810 cm² 287 cm

Answer 1

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

The surface area of a triangular prism can be calculated using the formula:

Surface Area = 2*(base area) + (perimeter of base * height)

First, we need to find the base area of the triangular prism. The base of the prism is a triangle with dimensions 13 cm, 9 cm, and 12 cm.

Area of a triangle can be calculated using Heron's formula:

s = (a + b + c) / 2
Area = sqrt[s * (s-a) * (s-b) * (s-c)]

s = (13 + 9 + 12) / 2 = 17

Area = sqrt[17 * (17-13) * (17-9) * (17-12)]
Area = sqrt[17 * 4 * 8 * 5]
Area = sqrt[5440]
Area = 73.78 cm²

Next, we need to find the perimeter of the base:

Perimeter = 13 + 9 + 12 = 34 cm

Now we can calculate the surface area of the triangular prism:

Surface Area = 2*(base area) + (perimeter of base * height)
Surface Area = 2*(73.78 cm²) + (34 cm * 5 cm)
Surface Area = 147.56 cm² + 170 cm²
Surface Area = 317.56 cm²

Therefore, 317.56 cm² of plastic wrap is needed to cover the wedge of cheese.