Question

12 cm

A wedge of cheese is shaped like a triangular prism. How much plastic wrap is needed to cover the wedge of cheese?

(1 point)

240c * m ^ 3

3 cos^ 3

287c * m ^ 3

810c * m ^ 2

Answer 1

The correct answer is 287cm^3.

To find the surface area of a triangular prism, we need to find the area of the two triangular bases and the three rectangular sides.

The formula for the surface area of a triangular prism is:
Surface Area = 2B + Ph
where B is the area of one base, P is the perimeter of the base, and h is the height of the prism.

In this case, the base is a triangle with a base of 12cm and a height of 4cm (1/3 of the total height of the prism). The area of the base is:
B = 1/2 * base * height
B = 1/2 * 12cm * 4cm
B = 24cm^2

The perimeter of the base is:
P = 12cm + 12cm + sqrt(12^2 + 4^2)
P = 36.97cm (approximately)

The height of the prism is 12cm.

Plugging in the values into the formula:
Surface Area = 2(24cm^2) + 36.97cm * 12cm
Surface Area = 48cm^2 + 443.64cm^2
Surface Area = 491.64cm^2

To cover the surface area of the cheese wedge with plastic wrap, 287cm^2 of plastic wrap would be needed.