This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.

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Answer
7
Here are the answers to your questions:
a) To find the number of different shapes, we identify each unique type of shape present in the image.
Step 1: Identify the unique shapes. • Pentagon (5 sides) • Rectangle (4 sides, 4 right angles) • Circle (round shape) • Parallelogram (4 sides, opposite sides parallel) • Hexagon (6 sides) • Trapezoid (4 sides, at least one pair of parallel sides) • Triangle (3 sides)
Step 2: Count the number of different types of shapes. There are 7 different types of shapes.
The list of shapes found is: • Pentagon • Rectangle • Circle • Parallelogram • Hexagon • Trapezoid • Triangle
The number of different shapes is .
b) Now, we count how many of each identified shape are present in the image.
Step 1: Count each shape. • Pentagon: 1 • Rectangle: 2 (one horizontal, one vertical) • Circle: 3 • Parallelogram: 2 • Hexagon: 1 • Trapezoid: 1 • Triangle: 3
The count for each shape is: • Pentagon: 1 • Rectangle: 2 • Circle: 3 • Parallelogram: 2 • Hexagon: 1 • Trapezoid: 1 • Triangle: 3
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This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.