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Geometric Operation Analogy - Intermediate Level: tricky scenarios handling Geometric Operation Analogy INTERMEDIATE

This expert challenge 📈 worksheet focuses on Geometric Operation Analogy - a key topic in Figure Analogy. You'll solve 20 intermediate-level problems (Worksheet 5 of 10). The primary focus is on tricky scenarios handling. Master how to solve geometric operation analogy, geometric operation analogy tricks, and geometric operation analogy shortcut methods through systematic practice.

📝 Worksheet 5 of 10 • 20 questions • ⏱️ Estimated time: 20 minutes • 🎯 Intermediate level

What you'll learn in this worksheet:
Your progress through Geometric Operation Analogy
Worksheet 5 of 10 (44% complete)

Question 1

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 2

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 3

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 4

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 5

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 6

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 7

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 8

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 9

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 10

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 11

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 12

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 13

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 14

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 15

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 16

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 17

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 18

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 19

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid

Question 20

Figure Analogy: A : B :: C : ? A shows circle UNION square, B shows their combined region. C shows hexagon + trapezoid. What is the union?
Step-by-Step Solution:

STEP 1: Understand Set Operation in A
- Component 1: Circle
- Operation symbol: + (indicates union/combination)
- Component 2: Rectangle
- Components: Overlapping or adjacent

STEP 2: Analyze Result in B
- Single unified region combining both shapes
- Overlapping area counted once (not double-shaded)
- Boundary: Outer perimeter of combined shape
- Operation: UNION (∪) in set theory = Combined area

STEP 3: Identify Components in C
- Component 1: Hexagon
- Operation symbol: + (same as in A)
- Component 2: Trapezoid
- Relationship: Adjacent or overlapping

STEP 4: Construct Union of C
- Merge hexagon and trapezoid
- Create single continuous region
- Outer boundary: Traces perimeter of combined shape
- Interior: All area covered by either polygon

Answer: Single merged region containing all area covered by either hexagon or trapezoid
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