Math Problem Statement
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 .
- The lateral faces are:
- Two faces of .
- Two faces of .
Step 2: Verify the Statements
-
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.
-
Option B: The lateral surface area is .
- Calculate the lateral surface area:
- Two faces: .
- Two faces: .
- Total lateral area: .
- False: The lateral surface area is not .
- Calculate the lateral surface area:
-
Option C: The dimensions of one of the bases are .
- True: The bases clearly match this dimension from the net.
-
Option D: The total surface area is .
- Calculate the total surface area:
- Bases: .
- Lateral area: .
- Total area: .
- True: The total surface area is .
- Calculate the total surface area:
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:
- How do you calculate the total surface area for a rectangular prism?
- What is the importance of congruent sides in three-dimensional shapes?
- Can you derive the formula for the surface area of a rectangular prism?
- What are some practical applications of calculating lateral surface areas?
- 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
-
Suitable Grade Level
Grade 7
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