Area of regular polygons int math 2

Front

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

Back

The area (A) of a regular polygon can be calculated using the formula: A = (1/2) * Perimeter * Apothem.

Front

Define a regular polygon.

Back

A regular polygon is a polygon that is equiangular (all angles are equal in measure) and equilateral (all sides have the same length).

Front

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

Back

The area of a regular hexagon can be calculated using the formula: A = (3√3/2) * s², where s is the side length. For s = 4 cm, A = (3√3/2) * 4² = 48√3 cm², approximately 83.14 cm².

Front

How do you find the perimeter of a regular polygon?

Back

The perimeter (P) of a regular polygon can be found by multiplying the number of sides (n) by the length of one side (s): P = n * s.

Front

What is the area of a regular octagon with a side length of 5 cm?

Back

The area of a regular octagon can be calculated using the formula: A = 2 * (1 + √2) * s². For s = 5 cm, A = 2 * (1 + √2) * 5² = 50(1 + √2) cm², approximately 50 * 2.414 = 120.7 cm².

Front

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

Back

The apothem is the perpendicular distance from the center of the polygon to a side. It is used in the area formula: A = (1/2) * Perimeter * Apothem.

Front

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

Back

The area of a regular pentagon can be calculated using the formula: A = (1/4) * √(5(5 + 2√5)) * s². For s = 6 cm, A = (1/4) * √(5(5 + 2√5)) * 6² = approximately 61.62 cm².

Front

What is the significance of the term 'regular' in regular polygons?

Back

The term 'regular' indicates that all sides and angles of the polygon are equal.

Front

How do you calculate the area of a regular dodecagon (12-sided polygon)?

Back

The area of a regular dodecagon can be calculated using the formula: A = 3 * s², where s is the side length. For example, if s = 3 cm, A = 3 * 3² = 27 cm².

Front

What is the area of a regular triangle (equilateral triangle) with a side length of 10 cm?

Back

The area of a regular triangle can be calculated using the formula: A = (√3/4) * s². For s = 10 cm, A = (√3/4) * 10² = 25√3 cm², approximately 43.30 cm².