Understanding Convex Equilateral Hexagons

The video tutorial explains how to solve a geometry problem involving a convex equilateral hexagon. It begins by defining the hexagon's properties and setting up the problem. The instructor then visualizes the hexagon on a coordinate plane, ensuring all vertices have distinct y-coordinates. Using trigonometry, the side length is calculated, followed by determining the hexagon's area. The solution involves understanding geometric properties, using trigonometric identities, and applying the Pythagorean theorem.

What is the definition of a convex equilateral hexagon?

• A hexagon with all sides equal and no angles equal

• A hexagon with all sides and angles equal

• A hexagon with all angles equal and no sides equal

• A hexagon with all sides equal and no interior angles greater than 180 degrees

Which y-coordinates are used for the vertices of the hexagon?

• 2, 4, 6, 8, 10, 12

• 0, 1, 2, 3, 4, 5

• 0, 2, 4, 6, 8, 10

• 1, 3, 5, 7, 9, 11

What is the relationship between the sides AB and DE?

• They intersect at a point

• They are equal in length

• They are parallel

• They are perpendicular

How is the angle FAB related to the angle on the left of the hexagon?

• FAB is 120 degrees less than the left angle

• FAB is 60 degrees more than the left angle

• FAB is 60 degrees less than the left angle

• FAB is equal to the left angle

What trigonometric identity is used to solve for S?

• Sine squared plus cosine squared equals one

• Tangent equals sine over cosine

• Cosine squared minus sine squared equals one

• Sine equals opposite over hypotenuse

What is the significance of the angle 120 degrees in the problem?

• It is the angle between a side and a diagonal

• It is the angle at vertex A

• It is the angle between two sides of the hexagon

• It is the angle between two diagonals

What is the base of the parallelogram within the hexagon?

• 10

• 8

• 6

• 4

How many triangles are used to calculate part of the hexagon's area?

• 5

• 2

• 3

• 4

What is the final form of the area of the hexagon?

• 64 square roots of 3

• 80 square roots of 3

• 144 square roots of 3

• 48 square roots of 3

What is the value of m plus n in the area expression?

• 50

• 49

• 51

• 48