Calculating Areas of Regular Polygons

This video tutorial explains how to calculate the area of regular polygons, including hexagons, pentagons, and equilateral triangles, using various methods. It covers scenarios where the apothem, side length, or radius is provided, and demonstrates calculations using trigonometry and geometry. The video also provides step-by-step examples for each type of polygon, ensuring a comprehensive understanding of the topic.

What is the formula to calculate the area of a regular polygon?

• Area = 0.5 * apothem * perimeter

• Area = apothem / perimeter

• Area = apothem + perimeter

• Area = perimeter / apothem

How many sides does a regular hexagon have?

• 3

• 5

• 4

• 6

What is the perimeter of a regular pentagon with each side measuring 10.6 units?

• 55 units

• 54 units

• 52 units

• 53 units

If a regular hexagon has a side length of 20, what is the length of each segment from the center to the midpoint of a side?

• 10 units

• 20 units

• 15 units

• 5 units

Using trigonometry, how can you find the apothem of a pentagon with a side divided by two measuring 15 units?

• Using the tangent function

• Using the secant function

• Using the sine function

• Using the cosine function

What is the area of an equilateral triangle with a side length of 20 using the simple formula?

• 50√3 square units

• 200√3 square units

• 150√3 square units

• 100√3 square units

How do you calculate the angle in a regular polygon with n sides?

• n / 360

• 360 / (2n)

• 360 / n

• 180 / n

What is the perimeter of a regular hexagon with a side length of 10?

• 70 units

• 50 units

• 40 units

• 60 units

If the radius of a circle is 24 cm, what is the side length of the inscribed equilateral triangle?

• 48√3 units

• 12√3 units

• 24√3 units

• 36√3 units

What is the area of a regular hexagon with an apothem of 5√3 and a perimeter of 60?

• 150√3 square units

• 100√3 square units

• 200√3 square units

• 250√3 square units