Area and Properties of Octagons

The video tutorial explains how to find the area of a regular octagon using its apothem. The process involves dividing the octagon into congruent triangles, calculating the angles and side lengths using trigonometry, and then finding the area of one triangle. This area is multiplied by the number of triangles to get the total area. The tutorial also discusses using formulas like 1/2 apothem times perimeter to find the area of regular polygons.

What is the first step in finding the area of the octagon?

• Use the area formula directly

• Calculate the perimeter

• Divide the octagon into triangles

• Find the length of the apothem

How many degrees is each central angle of the octagon?

• 30 degrees

• 45 degrees

• 90 degrees

• 60 degrees

What trigonometric function is used to find the base of the triangle?

• Sine

• Cosine

• Cotangent

• Tangent

What is the length of the base of the triangle after doubling?

• 2.5 units

• 5 units

• 7.5 units

• 10 units

What is the area of one triangle formed within the octagon?

• 20 square units

• 15 square units

• 25 square units

• 10 square units

How many triangles are formed when the octagon is divided?

• 6

• 7

• 9

• 8

What is the total area of the octagon?

• 120 square units

• 110 square units

• 130 square units

• 100 square units

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

• Area = 1/2 x base x height

• Area = apothem x perimeter

• Area = 1/2 x apothem x perimeter

• Area = base x height

How is the perimeter of the octagon related to the triangles?

• It is twice the base of one triangle

• It is the sum of all triangle bases

• It is the height of one triangle

• It is unrelated to the triangles

What is equivalent to the height of the triangle in the polygon formula?

• The central angle

• The perimeter

• The apothem

• The base