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 4 cm?

Back

Area = (3√3/2) * (4 cm)² = 41.57 cm².

Front

If a regular polygon has 8 sides, what is the measure of each interior angle?

Back

Each interior angle = (n-2) * 180° / n = (8-2) * 180° / 8 = 135°.

Front

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

Back

The apothem is the radius of the inscribed circle, while the radius is the distance from the center to a vertex.

Front

Calculate the area of a regular pentagon with a side length of 5 m and an apothem of 3.5 m.

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (5 m * 5) * 3.5 m = 43.75 m².

Front

What is the area of a regular dodecagon (12-sided polygon) with a side length of 2 m?

Back

Area = 3 * (2 m)² = 12√3 m² ≈ 20.78 m².

Front

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

Back

As the number of sides increases, the area approaches that of a circle with the same radius.

Front

What is the area of a regular octagon with an apothem of 6 m?

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (8 * 3 m) * 6 m = 72 m².