Triangle and Octagon Area Concepts

The video tutorial explains how to calculate the area of a regular octagon using its apothem. It begins by dividing the octagon into congruent triangles and calculating the central angles. The apothem splits each triangle, and the tangent function is used to find the side length. The area of one triangle is calculated and multiplied by the number of triangles to find the total area. The tutorial also introduces formulas for area calculation, such as 1/2 apothem times perimeter and 1/2 base times height.

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

• Calculate the perimeter

• Divide the octagon into triangles

• Use the area formula directly

• Find the length of the apothem

How many degrees is each central angle of the octagon?

• 45 degrees

• 30 degrees

• 60 degrees

• 90 degrees

What trigonometric function is used to find the side length of the triangle?

• Tangent

• Cotangent

• Cosine

• Sine

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

• 7.5 units

• 10 units

• 5 units

• 2.5 units

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

• 25 square units

• 20 square units

• 15 square units

• 10 square units

How many triangles are formed when the octagon is divided?

• 8

• 10

• 6

• 4

What is the total area of the octagon?

• 100 square units

• 130 square units

• 120 square units

• 110 square units

Which formula can be used to find the area of a regular polygon?

• Area = base x height

• Area = 1/2 x apothem x perimeter

• Area = 1/2 x base x height

• Area = apothem x perimeter

What does the 'n' represent in the formula 1/2 base x height x n?

• Number of sides

• Number of triangles

• Number of vertices

• Number of diagonals

What is equivalent to the perimeter in the formula 1/2 apothem x perimeter?

• n x area

• n x apothem

• n x height

• n x base