Polygons Answer Key

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📍 Part 1: Plotting and Identifying Polygons - ANSWERS

1. Plot the following points and connect them to form a polygon: A(2,3), B(5,3), C(5,6), D(2,6)

Answer: Rectangle (or quadrilateral). All angles are 90 degrees and opposite sides are equal.

2. What type of polygon is formed by connecting: E(-1,1), F(2,1), G(0,4)?

Answer: Triangle (specifically an isosceles triangle)

3. Plot and identify the polygon: H(-2,-1), I(1,-1), J(2,2), K(-1,2), L(-3,0)

Answer: Pentagon (5-sided polygon)

4. Which polygon has vertices at M(0,0), N(3,0), O(3,3), P(0,3)?

Answer: Square (all sides equal length of 3 units, all angles 90 degrees)

📏 Part 2: Calculating Side Lengths - ANSWERS

5. Find the length of side AB from question 1: A(2,3) to B(5,3)

Answer: 3 units (horizontal distance: 5 - 2 = 3)

6. Calculate the length of side EF from question 2: E(-1,1) to F(2,1)

Answer: 3 units (horizontal distance: 2 - (-1) = 3)

7. Find the length of the diagonal of the square in question 4: from M(0,0) to O(3,3)

Answer: Using distance formula: d = √[(3-0)² + (3-0)²]

d = √[9 + 9] = √18 = 3√2 ≈ 4.24 units

8. What is the perimeter of the rectangle from question 1?

Answer: Length = 3 units, Width = 3 units

Perimeter = 2(l + w) = 2(3 + 3) = 12 units

📝 Part 3: Word Problem - ANSWER

9. A city park is designed on a coordinate grid. The park boundaries form a quadrilateral with corners at (1,2), (6,2), (7,5), and (2,5). The city wants to install a fence around the entire perimeter. If each unit on the grid represents 10 feet, how many feet of fencing is needed?

Step 1: Calculate each side length

• Side 1: (1,2) to (6,2) = 5 units

• Side 2: (6,2) to (7,5) = √[(7-6)² + (5-2)²] = √[1 + 9] = √10 ≈ 3.16 units

• Side 3: (7,5) to (2,5) = 5 units

• Side 4: (2,5) to (1,2) = √[(1-2)² + (2-5)²] = √[1 + 9] = √10 ≈ 3.16 units

Step 2: Find perimeter in units

Perimeter = 5 + √10 + 5 + √10 = 10 + 2√10 ≈ 16.32 units

Step 3: Convert to feet

16.32 units × 10 feet/unit = 163.2 feet

10. What type of quadrilateral is the park?

Answer: Trapezoid (one pair of parallel sides: top and bottom sides are both horizontal)