Understanding Pick's Theorem and Polygon Area Calculation

What is the primary purpose of Pick's Theorem?

• To measure the angles of a polygon

• To calculate the perimeter of a polygon

• To determine the number of vertices in a polygon

• To find the area of a polygon

In Pick's Theorem, what does the variable 'I' represent?

• The number of vertices of the polygon

• The number of points on the boundary

• The number of interior points

• The total area of the polygon

How many interior points were found within the polygon?

• 44

• 34

• 29

• 22

What does the variable 'B' in Pick's Theorem stand for?

• The total area of the polygon

• The number of vertices

• The number of interior points

• The number of boundary points

How many points were located directly on the boundary of the polygon?

• 19

• 44

• 22

• 34

What is the first step in applying Pick's Theorem to find the area?

• Divide the boundary points by the interior points

• Multiply the interior points by the boundary points

• Add the interior and boundary points

• Subtract the boundary points from the interior points

What is the calculated area of the polygon using Pick's Theorem?

• 34 square units

• 22 square units

• 19 square units

• 44 square units

Which shapes were used to verify the area of the polygon?

• Square, rectangle, and circle

• Triangle, hexagon, and pentagon

• Rectangle, triangle, and trapezoid

• Circle, square, and rectangle

What is the area of the rectangle used in the verification method?

• 32 square units

• 44 square units

• 8 square units

• 4 square units

What is the total area of the polygon when verified using geometric methods?

• 34 square units

• 22 square units

• 44 square units

• 19 square units