Area of Regular Polygons

What is the significance of the apothem in calculating the area of a regular polygon?

• The apothem helps in determining the height of the triangles formed by dividing the polygon, which is essential for area calculation.

• The apothem is used to measure the perimeter of the polygon.

• The apothem determines the number of sides in the polygon.

• The apothem is irrelevant to the area calculation of a polygon.

What is the area of a triangle with a base of 10 cm and height of 5 cm?

• 20 cm²

• 25 cm²

• 30 cm²

• 15 cm²

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

• Area = (1/2) * Perimeter * Apothem

• Area = Base * Height

• Area = Side^2

• Area = (1/2) * Base * Height

Define 'regular polygon'.

• A polygon with all sides and angles equal.

• A polygon with unequal sides and angles.

• A polygon that has at least one right angle.

• A polygon that can be inscribed in a circle.

How do you calculate the area of a regular polygon with n sides?

• Area = (n * s * a) / 2, where s is the side length and a is the apothem.

• Area = n * s^2

• Area = (s^2 * n) / 4

• Area = n * (s + a)

How do you find the area of a regular dodecagon?

• Area = 3 * s², where s is the side length.

• Area = 6 * s², where s is the side length.

• Area = 4 * s², where s is the side length.

• Area = 2 * s², where s is the side length.

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

• 61.94 cm²

• 72.00 cm²

• 50.50 cm²

• 65.25 cm²

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

• 70.50 cm²

• 84.30 cm²

• 90.00 cm²

• 75.25 cm²

Define 'apothem' in the context of regular polygons.

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

• The length of a side of a regular polygon.

• The angle formed by two adjacent sides of a regular polygon.

• The area enclosed by a regular polygon.

What is the perimeter of a regular polygon?

• The area enclosed by the polygon.

• The total length of all the sides of the polygon.

• The number of sides multiplied by the length of one side.

• The sum of the interior angles of the polygon.