Areas 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 triangle with a base of 6 cm and a height of 4 cm?

Back

Area = (1/2) * base * height = (1/2) * 6 * 4 = 12 cm².

Front

What is the area of a square with a side length of 10 m?

Back

Area = side² = 10² = 100 m².

Front

How do you find the measure of each interior angle of a regular polygon?

Back

Interior angle = [(n-2) * 180°] / n, where n is the number of sides.

Front

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

Back

Area = (3√3/2) * side² = (3√3/2) * 4² = 24√3 cm².

Front

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

Back

The apothem is the height of the triangle formed by the radius and half of a side of the polygon.

Front

Calculate the area of a regular pentagon with a side length of 5 cm and an apothem of 6 cm.

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (5*5) * 6 = 75 cm².

Front

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

Back

Area = π * r², where r = 4√3/3 cm, so Area = π * (4√3/3)² = 16π/3 cm².