Exploring the Area of Polygons

The video tutorial explains how to calculate the area of regular polygons using a specific formula. It introduces the concept of a regular polygon, where all sides are equal, and explains the formula A = 1/2 * a * P, where 'a' is the apothem and 'P' is the perimeter. The apothem is defined as the line from the center to the midpoint of a side, forming a right angle. The tutorial demonstrates the calculation of the perimeter and area through examples, showing how the formula applies to different polygons like hexagons, septagons, and pentagons. The video concludes with a final example, reinforcing the method and emphasizing the flexibility of the formula across various polygon types.

What does a regular polygon imply about its sides?

• All sides are of different lengths

• All sides are of the same length

• All sides are parallel to each other

• All sides are perpendicular to each other

What does the 'P' in the area formula represent?

• Point of intersection

• Polygon count

• Perimeter

• Pi (π)

How is the area of a regular polygon calculated using the apothem?

• Multiply the apothem by the perimeter and then divide by 2

• Divide the apothem by the perimeter

• Add the apothem to the perimeter

• Multiply the apothem by the number of sides

What geometric shape is used to derive the area formula for regular polygons?

• Triangle

• Circle

• Square

• Rectangle

If a hexagon has a side length of 14 units, what is its perimeter?

• 84 units

• 28 units

• 140 units

• 72 units

What is the area of a polygon with an apothem of 16 units and a perimeter of 107.8 units?

• 856 units squared

• 862.4 units squared

• 1712 units squared

• 431.2 units squared

How many sides does a septagon have?

• 7

• 5

• 6

• 8

What is the area of a regular polygon with 7 sides, each 15.4 units long, and an apothem of 16 units?

• 249 units squared

• 862.4 units squared

• 431.2 units squared

• 107.8 units squared

Does the order of multiplication affect the result in the area formula of a polygon?

• No, but it affects the units of measurement

• Yes, but only for polygons with more than 6 sides

• Yes, it changes the result significantly

• No, multiplication is commutative

What is the correct calculation for the area of a pentagon with an apothem of 5 units and a side length of 8 units?

• 160 units squared

• 200 units squared

• 249 units squared

• 40 units squared