Calculating the Area of Regular Polygons

The video tutorial explains how to find the area of any regular polygon using the formula: area = 1/2 * apothem * perimeter. It demonstrates this process with examples of a regular hexagon and a regular octagon. For the hexagon, the apothem is 7 inches and each side is 8 inches, resulting in an area of 168 square inches. For the octagon, the apothem is 6 inches and each side is 5 inches, resulting in an area of 120 square inches. The tutorial emphasizes understanding the apothem and perimeter calculations for accurate area determination.

What is multiplied with the apothem to find the area of a regular polygon?

• The polygon's diameter

• The polygon's radius

• The polygon's perimeter

• The polygon's number of sides

What is the apothem of a polygon?

• The length of the longest side

• The longest diagonal of the polygon

• The distance from the center to a vertex

• The distance from the center to the midpoint of a side

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

• 1/2 * apothem * side length

• 1/2 * apothem * perimeter

• Apothem * perimeter

• 1/2 * perimeter / apothem

What is the perimeter of a regular hexagon with each side measuring 8 inches?

• 48 inches

• 24 inches

• 64 inches

• 32 inches

How many sides does a regular hexagon have?

• 8

• 6

• 4

• 5

How do you find the area of a regular hexagon with an apothem of 7 inches and a perimeter of 48 inches?

• Add 7 to 48 and then divide by 2

• Divide 7 by 48 and then multiply by 2

• Multiply 7 by 48 and then multiply by 2

• Multiply 7 by 48 and then divide by 2

What is the final step in calculating the area of a regular polygon using the given formula?

• Add 2 to the result

• Divide the result by 2

• Subtract 2 from the result

• Multiply the result by 2

What is the perimeter of a regular octagon with each side measuring 5 inches?

• 20 inches

• 80 inches

• 40 inches

• 10 inches

How do you calculate the area of a regular octagon with an apothem of 6 inches and a perimeter of 40 inches?

• Multiply 6 by 40 and then divide by 2

• Multiply 6 by 40 and then multiply by 2

• Divide 6 by 40 and then multiply by 2

• Add 6 to 40 and then divide by 2

What simplification technique is used in the final step of calculating the area of a regular octagon?

• Multiplying the perimeter by 2

• Doubling the apothem length

• Ignoring the zero and halving the remaining number

• Dividing the apothem by 2