Practice worksheet for calculating the area of regular polygons using the apothem and perimeter formula.

To find the area of each regular polygon, we use the formula given in the worksheet:

Area = 1/2 × (apothem × perimeter)

We are told that the apothem is already rounded off, so we’ll use the given values as-is.

For each shape:
- Perimeter = number of sides × side length
- Then plug into: Area = 0.5 × apothem × perimeter

Let’s go one by one.

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Top Row:

1. Heptagon (7 sides), side = 7 cm, apothem = 7.3 cm
Perimeter = 7 × 7 = 49 cm
Area = 0.5 × 7.3 × 49 = 0.5 × 357.7 = 178.85 cm²

2. Hexagon (6 sides), side = 6 cm, apothem = 5.2 cm
Perimeter = 6 × 6 = 36 cm
Area = 0.5 × 5.2 × 36 = 0.5 × 187.2 = 93.6 cm²

3. Heptagon (7 sides), side = 9 cm, apothem = 9.3 cm
Perimeter = 7 × 9 = 63 cm
Area = 0.5 × 9.3 × 63 = 0.5 × 585.9 = 292.95 cm²

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Middle Row:

4. Pentagon (5 sides), side = 3 cm, apothem = 2.1 cm
Perimeter = 5 × 3 = 15 cm
Area = 0.5 × 2.1 × 15 = 0.5 × 31.5 = 15.75 cm²

5. Octagon (8 sides), side = 5 cm, apothem = 6 cm
Perimeter = 8 × 5 = 40 cm
Area = 0.5 × 6 × 40 = 0.5 × 240 = 120 cm²

6. Hexagon (6 sides), side = 5 cm, apothem = 4.3 cm
Perimeter = 6 × 5 = 30 cm
Area = 0.5 × 4.3 × 30 = 0.5 × 129 = 64.5 cm²

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Bottom Row:

7. Octagon (8 sides), side = 7 cm, apothem = 8.4 cm
Perimeter = 8 × 7 = 56 cm
Area = 0.5 × 8.4 × 56 = 0.5 × 470.4 = 235.2 cm²

8. Pentagon (5 sides), side = 10 cm, apothem = 6.9 cm
Perimeter = 5 × 10 = 50 cm
Area = 0.5 × 6.9 × 50 = 0.5 × 345 = 172.5 cm²

9. Pentagon (5 sides), side = 2 cm, apothem = 1.4 cm
Perimeter = 5 × 2 = 10 cm
Area = 0.5 × 1.4 × 10 = 0.5 × 14 = 7 cm²

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Final Answer:
178.85 cm², 93.6 cm², 292.95 cm², 15.75 cm², 120 cm², 64.5 cm², 235.2 cm², 172.5 cm², 7 cm²