Triangles and Areas in Polygons

The video tutorial explains how to find the area of a regular polygon by dividing it into congruent triangles. Using a pentagon as an example, the teacher demonstrates how to calculate the area of one triangle using the formula 1/2 base times height, where the base is a side of the polygon and the height is the apothem. The total area of the polygon is found by multiplying the area of one triangle by the number of triangles, which equals the number of sides of the polygon.

What is a key characteristic of a regular polygon?

• It has an odd number of sides.

• It has congruent sides and angles.

• It has sides of different lengths.

• It has only right angles.

How do you calculate the area of a triangle?

• Base times height

• Base divided by height

• Half of base times height

• Base plus height

What is the apothem in a regular polygon?

• The perimeter of the polygon

• The height of a triangle within the polygon

• The radius of the circumscribed circle

• The longest side of the polygon

How many triangles can be formed in a regular pentagon?

• Five

• Six

• Four

• Three

What is the relationship between the number of sides and the number of triangles in a regular polygon?

• The number of triangles is half the number of sides.

• The number of triangles is always double the number of sides.

• The number of triangles is equal to the number of sides.

• The number of triangles is always one less than the number of sides.

If a regular polygon has sides of 10 meters and an apothem of 8 meters, what is the area of one triangle?

• 50 square meters

• 30 square meters

• 40 square meters

• 20 square meters

What is the total area of a regular pentagon with five triangles each having an area of 40 square meters?

• 100 square meters

• 150 square meters

• 200 square meters

• 250 square meters

How can the method of finding the area of a regular polygon be generalized?

• By calculating the perimeter first

• By using only the apothem

• By dividing the polygon into congruent triangles

• By using different formulas for different polygons

What must be true for the method of dividing into triangles to work for any regular polygon?

• All sides must be different.

• All angles must be right angles.

• All sides and angles must be congruent.

• The polygon must have an even number of sides.

What is the first step in finding the area of a regular polygon?

• Divide the polygon into triangles

• Draw a circle around the polygon

• Find the length of the apothem

• Calculate the perimeter