Gripline Gym: Nets and Surface Area

Plan coverings for skate features, climbing markers, and member equipment.

A Skate Feature Cover

Use the net for Questions 1–3. All measurements are in feet. Ignore seams, overlaps, and material thickness throughout the worksheet.

Gripline Gym is covering a closed rectangular skate feature. Each label gives a face's length × width. The grid squares have side lengths of 1 foot.

What are the three dimensions of the feature formed by this net?

A. 12 ft, 7 ft, and 1 ftB. 8 ft, 4 ft, and 6 ftC. 4 ft, 3 ft, and 3 ftD. 4 ft, 2 ft, and 3 ft

The two 4 × 2 faces will receive a different coating from the other faces.

What is the combined area of these two faces? square feet

What is the total surface area of the closed feature? square feet

A smaller closed skate feature is a rectangular prism measuring 5 ft by 3 ft by 2 ft. Draw one connected net that folds into this prism without overlapping faces. Label the dimensions of all six faces. Your sketch does not need to be to scale.

Climbing Route Markers

Use the dimensions given for each design. Include every face of a closed solid unless the question says otherwise.

A large climbing route marker is a closed triangular prism. Each triangular end is a right triangle with perpendicular sides of 3 cm and 4 cm and a third side of 5 cm. The prism is 8 cm long. Draw one connected net with all five faces. Label each rectangle's dimensions and all three side lengths of each triangle. Mark the right angles. Your sketch does not need to be to scale.

For the triangular prism in Question 5, which expression includes the area of every face exactly once?

A. 3 × 8 + 4 × 8 + 5 × 8 + 2 × (1/2 × 3 × 4)B. 3 × 8 + 4 × 8 + 5 × 8 + 2 × (3 × 4)C. 2 × (3 × 8 + 4 × 8 + 5 × 8) + 2 × (1/2 × 3 × 4)D. 3 × 8 + 4 × 8 + 5 × 8 + 1/2 × 3 × 4

What is the surface area of the triangular prism in Question 5? square centimeters

Another route marker is a square pyramid. Its net consists of one square with a 6-cm side and four congruent triangles, one attached to each square edge. Each triangle has a base of 6 cm and a perpendicular height of 5 cm.

What is the total area of this net? square centimeters

The pyramid in Question 8 has a vertical height of 4 cm, measured inside the solid. Luis uses 4 cm instead of 5 cm to find each triangular face's area. Which statement correctly identifies his mistake?

A. He should use 9 cm because the two given heights must be added.B. He should use 5 cm because the needed height lies in the triangular face.C. He should use 6 cm because the triangle's base also gives its height.D. He should use 4 cm because the solid's height lies in every triangular face.

Member Equipment Decisions

Use face areas to make each decision. For the final question, explain how the proposed net would fold.

10.

Members return rental gear to an open-top rectangular bin. Its bottom measures 6 dm by 4 dm, and its height is 3 dm. Staff will cover the outside bottom and all four outside walls, but there is no lid.

What area must be covered? square decimeters

11.

Staff need to cover two closed triangular route markers. Each marker has right-triangle ends with perpendicular sides of 3 cm and 4 cm and a third side of 5 cm. Each prism is 8 cm long. Staff have 200 square centimeters of covering material. Assume every piece can be used.

How much additional material is needed? square centimeters

12.

The membership desk needs a closed box for wristbands. One design is a cube with 4-inch edges. Another is a rectangular prism measuring 6 inches by 4 inches by 2 inches. Material costs the same per square inch. Which comparison is correct?

A. The cube uses 8 square inches less material than the rectangular prism.B. The cube uses 16 square inches less material than the rectangular prism.C. The rectangular prism uses 8 square inches less material than the cube.D. The rectangular prism uses 16 square inches less material than the cube.

13.

Nia plans a cube-shaped membership display with 2-inch edges. She draws six 2-inch squares in one straight row, with neighboring squares sharing full edges. She says, “The area is 24 square inches, so this must be a valid cube net.” Is her area calculation correct? Is her net valid? Explain why the area calculation alone does not settle whether the net works.