Area of regular polygons

Front

What is the apothem of a regular polygon?

Back

The apothem is the distance from the center of the polygon to the midpoint of one of its sides.

Front

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

Back

A = ½ ∙ P ∙ a, where A is the area, P is the perimeter, and a is the apothem.

Front

How do you calculate the area of a regular hexagon with a side length of 6 units?

Back

Area = ½ ∙ P ∙ a = ½ ∙ (6*6) ∙ (3√3) ≈ 93.53 square units.

Front

What is the perimeter of a regular polygon with 8 sides, each of length 5 units?

Back

Perimeter (P) = number of sides × length of one side = 8 × 5 = 40 units.

Front

If the apothem of a regular pentagon is 4 units and the perimeter is 20 units, what is the area?

Back

Area = ½ ∙ P ∙ a = ½ ∙ 20 ∙ 4 = 40 square units.

Front

What is the area of a regular octagon with a side length of 3 units?

Back

Area = 2(1 + √2) × (side length)² = 2(1 + √2) × 3² ≈ 2(1 + 1.414) × 9 ≈ 2(2.414) × 9 ≈ 43.45 square units.

Front

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

Back

The apothem is the shortest distance from the center to a side, while the radius is the distance from the center to a vertex.

Front

How do you find the area of a regular dodecagon (12-sided polygon) with a side length of 2 units?

Back

Area = 3 × (2 + 2√3) × (side length)² = 3 × (2 + 2√3) × 2² ≈ 20.78 square units.

Front

What is the area of a regular triangle (equilateral triangle) with a side length of 4 units?

Back

Area = (√3/4) × (side length)² = (√3/4) × 4² = 4√3 ≈ 6.93 square units.

Front

If a regular polygon has an area of 50 square units and an apothem of 5 units, what is the perimeter?

Back

Using A = ½ ∙ P ∙ a, we find P = (2A)/a = (2 × 50)/5 = 20 units.