Trigonometry and Geometry of Polygons

The video tutorial explains how to find the surface area of an octagonal prism using a formula similar to that of a hexagonal prism. It covers calculating the base area using the apothem and trigonometry, and the lateral area by unfolding the prism into a rectangle. The tutorial provides a step-by-step guide with measurements and calculations, including helpful hints for other shapes like pentagons.

What is the basic formula for finding the surface area of an octagonal prism?

• 2 times the base area plus lateral area

• Base area plus lateral area

• Base area times height

• Perimeter times height

How do you find the central angle of an octagon?

• Divide 180 by 6

• Divide 180 by 8

• Divide 360 by 8

• Divide 360 by 6

What trigonometric function is used to find the apothem of an octagon?

• Secant

• Tangent

• Cosine

• Sine

If one side of the octagon is 8, what is the perimeter of the octagonal base?

• 32

• 80

• 48

• 64

What is the formula for calculating the lateral area of an octagonal prism?

• Perimeter plus base area

• Base area times height

• Perimeter times height

• 2 times base area

What is the total surface area of the octagonal prism if the base area is 62.8 and the lateral area is 768?

• 7680

• 13888

• 1388.8

• 830.8

What is the central angle of a pentagon?

• 90 degrees

• 72 degrees

• 45 degrees

• 36 degrees

How do you calculate the central angle for any polygon?

• Multiply 180 by the number of sides

• Divide 180 by the number of sides

• Multiply 360 by the number of sides

• Divide 360 by the number of sides

What is the angle used in trigonometry for a pentagon when calculating the apothem?

• 72 degrees

• 45 degrees

• 18 degrees

• 36 degrees

Which trigonometric ratio is used to find the apothem when the side length is known?

• Cosine

• Cotangent

• Sine

• Tangent