Jordan purchased a piece of fabric that is 18 cm by 18 cm in order to make a tent for her little sister’s dolls. Using the dimensions for the tent shaped as a triangular prism, how much fabric will be left over?

Question

(1 point)
Responses

324 cm2
  324 cm squared

184 cm2
  184 cm squared

84 cm2
84 cm squared

240 cm2

Answer 1

In order to find the total amount of fabric needed for the triangular prism tent, we need to calculate the surface area of the shape.

Formula for the surface area of a triangular prism:
Surface Area = 2 * (area of triangle base) + (perimeter of base * height)

Given that the fabric is 18 cm by 18 cm, we know that it forms an equilateral triangle. Calculating the area of an equilateral triangle:

Area of triangle base = (√3/4) * (side length)^2
Area of triangle base = (√3/4) * (18)^2
Area of triangle base = (√3/4) * 324
Area of triangle base = 81√3

Since all sides of an equilateral triangle are equal, the perimeter of the base is 3 * side length:
Perimeter of base = 3 * 18
Perimeter of base = 54 cm

Height of the prism is also 18 cm.

Surface Area = 2 * 81√3 + (54 * 18)
Surface Area = 162√3 + 972

Surface Area = 162.442 + 972
Surface Area = 1134.442 cm^2

The total amount of fabric needed for the tent would be 1134.442 cm^2. Since she purchased a piece of fabric that is 18 cm by 18 cm (324 cm^2), the amount of fabric left over would be:
324 cm^2 - 1134.442 cm^2 = 810 cm^2

The amount of fabric left over is 810 cm^2.

Which is not among the listed multiple-choice options.