Math Problem Statement

The net of a rectangular prism and its dimensions in feet are shown. Which of the following is NOT a true statement about the figure?

Solution

Let's analyze the question and solve it.

Given:

  • The net of a rectangular prism is shown, with dimensions labeled:
    • 2 ft (length)
    • 1.5 ft (width)
  • The task is to identify the NOT true statement from the provided choices.

Step 1: Dimensions of the Prism

From the net:

  • Two opposite bases are 3.5ft×1.5ft3.5 \, \text{ft} \times 1.5 \, \text{ft}.
  • The lateral faces are:
    • Two faces of 2ft×1.5ft2 \, \text{ft} \times 1.5 \, \text{ft}.
    • Two faces of 2ft×3.5ft2 \, \text{ft} \times 3.5 \, \text{ft}.

Step 2: Verify the Statements

  1. Option A: The prism has two pairs of congruent sides.

    • True: The bases and lateral faces come in pairs with identical dimensions, so the prism has congruent sides.
  2. Option B: The lateral surface area is 24.5square feet24.5 \, \text{square feet}.

    • Calculate the lateral surface area:
      • Two faces: 2ft×1.5ft=3sq. ft each2 \, \text{ft} \times 1.5 \, \text{ft} = 3 \, \text{sq. ft each}.
      • Two faces: 2ft×3.5ft=7sq. ft each2 \, \text{ft} \times 3.5 \, \text{ft} = 7 \, \text{sq. ft each}.
      • Total lateral area: 23+27=6+14=20sq. ft2 \cdot 3 + 2 \cdot 7 = 6 + 14 = 20 \, \text{sq. ft}.
    • False: The lateral surface area is not 24.5sq. ft24.5 \, \text{sq. ft}.
  3. Option C: The dimensions of one of the bases are 3.5ft×1.5ft3.5 \, \text{ft} \times 1.5 \, \text{ft}.

    • True: The bases clearly match this dimension from the net.
  4. Option D: The total surface area is 30.5square feet30.5 \, \text{square feet}.

    • Calculate the total surface area:
      • Bases: 2(3.51.5)=25.25=10.5sq. ft2 \cdot (3.5 \cdot 1.5) = 2 \cdot 5.25 = 10.5 \, \text{sq. ft}.
      • Lateral area: 20sq. ft20 \, \text{sq. ft}.
      • Total area: 10.5+20=30.5sq. ft10.5 + 20 = 30.5 \, \text{sq. ft}.
    • True: The total surface area is 30.5sq. ft30.5 \, \text{sq. ft}.

Step 3: Conclusion

The statement that is NOT true is Option B: The lateral surface area is 24.5 square feet.


Would you like me to elaborate further or break down any calculations? Here are 5 related questions to expand your understanding:

  1. How do you calculate the total surface area for a rectangular prism?
  2. What is the importance of congruent sides in three-dimensional shapes?
  3. Can you derive the formula for the surface area of a rectangular prism?
  4. What are some practical applications of calculating lateral surface areas?
  5. How would the calculations change if one of the dimensions of the net was doubled?

Tip: Always verify each part of a multi-step problem to avoid errors in large calculations.

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Math Problem Analysis

Mathematical Concepts

Geometry
Surface Area
Rectangular Prisms

Formulas

Surface Area = 2(lb + bh + hl)
Lateral Surface Area = Perimeter of Base x Height

Theorems

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Suitable Grade Level

Grade 7