Polygon Area Master

Find the area of a regular pentagon with side length 6 cm.

Solution:

Area = 1.72 × s²

Area = 1.72 × 6²

Area = 1.72 × 36

Area = 61.92 cm²

Find the area of a regular hexagon with side length 4 cm.

Solution:

Area = 2.598 × s²

Area = 2.598 × 4²

Area = 2.598 × 16

Area = 41.57 cm²

Find the area of a regular pentagon with side length 8 cm and apothem 5.5 cm.

Solution:

Area = (5 × s × a) ÷ 2

Area = (5 × 8 × 5.5) ÷ 2

Area = (220) ÷ 2

Area = 110 cm²

Find the area of a regular hexagon with radius 7 cm.

Solution:

Area = (3 × √3 × r²) ÷ 2

Area = (3 × 1.732 × 7²) ÷ 2

Area = (3 × 1.732 × 49) ÷ 2

Area = 127.3 cm²

For regular pentagons, you can use the approximation:

Area ≈ 1.72 × s²

For regular hexagons, you can use:

Area ≈ 2.6 × s²

These approximations are accurate enough for most calculations.

For a regular pentagon:

- Apothem ≈ 0.688 × side length

- Radius ≈ 0.851 × side length

For a regular hexagon:

- Apothem = 0.866 × side length

- Radius = side length

For any regular polygon with n sides:

Area = (n × s × a) ÷ 2

Where n = number of sides, s = side length, a = apothem

This works for both pentagons (n=5) and hexagons (n=6).

If you know multiple measurements, calculate the area using different formulas to verify your answer.

For example, if you know both the side length and apothem of a hexagon, calculate the area using both the s² formula and the (n×s×a)÷2 formula.