Topic 50 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 an apothem in the context of regular polygons?

Back

The apothem is the distance from the center of the 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 pentagon with a side length of 6 cm and an apothem of 4.5 cm?

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (5 * 6) * 4.5 = 67.5 cm².

Front

If a regular hexagon has a side length of 10 m, what is its area?

Back

Area = (3√3/2) * (side length)² = (3√3/2) * (10)² = 259.8 m².

Front

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

Back

Area = 2(1 + √2) * (side length)² = 2(1 + √2) * (5)² = 98.99 m².

Front

Find the area of a regular polygon with 8 sides, each measuring 4 cm, and an apothem of 5 cm.

Back

Area = (1/2) * Perimeter * Apothem = (1/2) * (8 * 4) * 5 = 80 cm².

Front

What is the area of a regular dodecagon (12 sides) with a side length of 3 m?

Back

Area = 3 * (2 + √3) * (side length)² = 3 * (2 + √3) * (3)² = 31.18 m².

Front

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

Back

Increasing the number of sides generally increases the area, approaching the area of a circle as the number of sides becomes very large.