Area of Regular Polygons

Front

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

Back

Area = (1/2) * Perimeter * Apothem

Front

Define a regular polygon.

Back

A regular polygon is a polygon with all sides and angles equal.

Front

What is the perimeter of a regular polygon with 6 sides, each measuring 10 cm?

Back

Perimeter = 6 * 10 cm = 60 cm.

Front

How do you find the apothem of a regular polygon?

Back

The apothem can be found using the formula: Apothem = (side length) / (2 * tan(π/n)), where n is the number of sides.

Front

Calculate the area of a regular hexagon with a side length of 10 cm.

Back

Area = (3√3/2) * (side length)² = (3√3/2) * (10)² = 150√3 cm².

Front

What is the area of a regular pentagon with a side length of 8 cm?

Back

Area = (5/4) * (side length)² * (cot(π/5)) = 27.527 cm².

Front

If the area of a regular octagon is 128 cm², what is the side length?

Back

Side length = √(Area * 4/(2 + 2√2)) = 5.656 cm.

Front

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

Back

The area can be calculated using the apothem and the perimeter: Area = (1/2) * Perimeter * Apothem.

Front

Find the area of a regular dodecagon (12 sides) with a side length of 5 cm.

Back

Area = 3 * (2 + √3) * (side length)² = 75 cm².

Front

What is the area of a regular triangle (equilateral) with a side length of 6 cm?

Back

Area = (√3/4) * (side length)² = 15.588 cm².