Question

6 cm

7 cm

12 cm

4 cm

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?

(1 point)

O 324 cm2

O 240 cm2

O 184 cm2

O 84 cm2

Answer 1

I don’t see the diagram, so I’m not sure which of the four numbers is the prism’s length and which three are the triangle’s side lengths. The fabric needed = surface area of the triangular prism = 2·(area of triangle) + (perimeter of triangle)·(prism length). Leftover = 18·18 − (fabric used).

Two reasonable interpretations of your four numbers give different answers:

1) If the prism length = 4 cm and the triangular face has sides 6, 7, 12:
- Triangle area (Heron): s = 12.5, area ≈ 14.97 cm², so 2 triangles ≈ 29.94 cm².
- Rectangles: (6+7+12)·4 = 25·4 = 100 cm².
- Total fabric used ≈ 129.94 cm² → leftover ≈ 324 − 129.94 = 194.06 cm².

2) If the prism length = 12 cm and the triangular face has sides 4, 6, 7:
- Triangle area (Heron): s = 8.5, area ≈ 11.97 cm², so 2 triangles ≈ 23.94 cm².
- Rectangles: (4+6+7)·12 = 17·12 = 204 cm².
- Total fabric used ≈ 227.94 cm² → leftover ≈ 324 − 227.94 = 96.06 cm².

Neither of those matches the multiple-choice options you listed. Please either upload or describe the original diagram (which side is the prism length, and which three values label the triangle), and confirm whether the tent includes the bottom face; then I’ll compute the exact leftover and pick the correct choice.