Question

12 yd.

13 yd.

11 yd.

5 yd.

What is the surface area of the triangular prism?

(1 point)

240 square yards

330 square yards

390 square yards

360 square yards

Answer 1

A hot chocolate company is deciding which box shape to use for

measures 8 inches by 6 inches by 9 inches. The second box (BoxB) measures 9 inches by 4 inches by 13 inches. Which box requires more material to make? (1 point)

Box A requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 205 square inches.

Both Box A and Box B require the same amount of material.

Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 366 square inches.

Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches

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Answer 2

To find the surface area of a triangular prism, you need to calculate the areas of the three rectangular faces and the two triangular faces.

For the rectangular faces:
- Area = length x width

Rectangle 1: 12 yd. x 5 yd. = 60 sq. yd.
Rectangle 2: 13 yd. x 5 yd. = 65 sq. yd.
Rectangle 3: 11 yd. x 5 yd. = 55 sq. yd.

For the triangular faces:
- Area = (1/2) x base x height

Triangle 1 (base = 12 yd., height = 11 yd.): (1/2) x 12 yd. x 11 yd. = 66 sq. yd.
Triangle 2 (base = 13 yd., height = 5 yd.): (1/2) x 13 yd. x 5 yd. = 32.5 sq. yd.

Total surface area = 60 sq. yd. + 65 sq. yd. + 55 sq. yd. + 66 sq. yd. + 32.5 sq. yd. = 278.5 sq. yd.

Therefore, the surface area of the triangular prism is approximately 278.5 square yards. None of the provided options are correct.

Answer 3

To determine which box requires more material, we need to calculate the surface area of each box.

For Box A:
- Total surface area = 2(lw + lh + wh)
- Total surface area = 2(8x6 + 8x9 + 6x9)
- Total surface area = 2(48 + 72 + 54)
- Total surface area = 2(174)
- Total surface area = 348 square inches

For Box B:
- Total surface area = 2(lw + lh + wh)
- Total surface area = 2(9x4 + 9x13 + 4x13)
- Total surface area = 2(36 + 117 + 52)
- Total surface area = 2(205)
- Total surface area = 410 square inches

Therefore, Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches.

So, the correct answer is:
- Box B requires more material to make because the total material needed for Box A is 348 square inches, and the total material needed for Box B is 410 square inches.