Question

Sasha is making custom designs using these small trapezoidal prisms. She wants to cover each of the 8 prisms in her current design in striped cloth on all sides. She has 3500 square centimeters of striped cloth.
Does Sasha have enough cloth to cover all 8 prisms in her current design?

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The combined surface area of the prisms is cm², therefore Sasha have enough cloth for her current design.

Answer 1

Answer:

The combined surface area of the prisms is 3040 cm², therefore Sasha does have enough cloth for her current design.

Step-by-step explanation:

7 + 6 = 13                (Length + Height)

13 x 5 = 65              side a (h + l)

15 x 13 = 195           side b (h+l)

10 x 6 = 60             side c x length

10 x 6 = 60             side d x length

All of the above added together is 380, one trapezoidal prism.

380 x 8 = 3040

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Answer 2

Combined surface area for the 8 prisms is: 3,040 square centimeters.

3,500 cm² > 3,040 cm², therefore, Sasha has enough cloth for the design.

What is the Surface Area of a Trapezoidal Prism?

Surface area = (b1 + b2)h + PH

Given the following dimensions:

• b1 = 5 cm
• b2 = 15 cm
• Height of trapezium (h) = 7 cm
• Perimeter of trapezium (P) = 15 + 10 + 10 + 5 = 40 cm
• Height of prism (H) = 6 cm

Plug in the values into SA = (b1 + b2)h + PH:

Surface area = (5 + 15)7 + (40)(6)

Surface area = 380 sq. cm.

Combined surface area for the 8 prisms = 380 × 8 = 3,040 square centimeters.

3,500 cm² > 3,040 cm², therefore, Sasha has enough cloth.

Learn more about surface area of trapezoidal prism on:

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