Math Problem Statement
Solution
To solve this problem, let's go step by step.
Step 1: Apply the Zoom Factor of 2
When a geometric shape is enlarged by a zoom factor of 2, each of its side lengths is multiplied by 2.
The original side lengths are:
- 4, 3, 6, and 5.
After applying the zoom factor of 2:
Step 2: Calculate the Perimeter of the New Figure
The perimeter is the sum of all side lengths.
Thus, the perimeter of the new figure is 36 units.
Step 3: Calculate the Area of the New Figure
The shape resembles a trapezoid, with two parallel sides (3 and 6 originally) and height 4.
Original Area of the Trapezoid:
Using the formula for the area of a trapezoid:
Where:
Area of the Enlarged Figure:
Since the enlargement factor is 2, the area will increase by times.
Final Answers:
- Perimeter of the new figure: 36 units.
- Area of the new figure: 72 square units.
Do you need any further details or have any questions?
Here are some follow-up questions you might find helpful:
- How does the area scale with different zoom factors?
- How would the perimeter change with a zoom factor of 3 instead?
- What if the shape was rotated—would the perimeter or area change?
- Can you confirm if all shapes scale similarly with zoom factors?
- How would we calculate the side lengths if the original diagram had missing measurements?
Tip: Remember that area scales with the square of the zoom factor, while perimeter scales linearly!
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Math Problem Analysis
Mathematical Concepts
Geometry
Scaling
Perimeter
Area
Formulas
Perimeter = sum of all side lengths
Area of a trapezoid = (1/2) * (b1 + b2) * h
Theorems
Scaling Theorem for Perimeter and Area
Suitable Grade Level
Grades 6-8
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