Area of Regular Polygons

Front

What is the formula for the area of a regular polygon?

Back

Area = (1/2) * Perimeter * Apothem

Front

Define 'apothem' in the context of regular polygons.

Back

The apothem is the distance from the center of a regular polygon to the midpoint of one of its sides.

Front

How do you calculate the perimeter of a regular polygon?

Back

Perimeter = Number of sides * Length of one side.

Front

What is the area of a regular hexagon with a side length of 6 cm?

Back

Area = (3√3/2) * (6 cm)² = 93.53 cm².

Front

If a regular polygon has an apothem of 10 cm and a perimeter of 40 cm, what is its area?

Back

Area = (1/2) * 40 cm * 10 cm = 200 cm².

Front

What is the relationship between the apothem and the area of a regular polygon?

Back

The area of a regular polygon can be calculated using the apothem and the perimeter.

Front

Find the area of a regular pentagon with a side length of 5 cm and an apothem of 6.88 cm.

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (5 cm * 5) * 6.88 cm = 86.1 cm².

Front

What is the area of a regular octagon with a side length of 4 cm?

Back

Area = 2(1 + √2) * (4 cm)² = 64.0 cm².

Front

How does increasing the number of sides of a regular polygon affect its area?

Back

Generally, as the number of sides increases, the area of the polygon increases, approaching the area of a circle.

Front

What is the area of a regular dodecagon (12 sides) with a side length of 3 cm?

Back

Area = 3 * (3 cm)² = 27√3 cm² ≈ 46.76 cm².