Regular Polygons and Their Properties

What is the ratio of the sides in a 45-45-90 triangle?

• 1:1:√2

• 1:√3:2

• 1:1:1

• 1:2:√3

If the hypotenuse of a 45-45-90 triangle is 16√2, what is the length of each leg?

• 8

• 32

• 16

• 16√2

How many sides does a regular hexagon have?

• 5

• 8

• 4

• 6

What is the perimeter of a hexagon if one side is 16√3/3?

• 32√3

• 96√3

• 48√3

• 64√3

What is the area of a hexagon with a perimeter of 32√3 and an apothem of 8?

• 128√3

• 32√3

• 64√3

• 256√3

What is the perimeter of a regular hexagon with an area of 54√3 units squared?

• 72

• 54

• 36

• 18

If the area of a regular hexagon is 54√3, what is the length of one side?

• 12

• 9

• 3

• 6

Can a regular octagon have an area of 10 units squared?

• Only if the side length is 10

• Yes, with integral side lengths

• Yes, but not with integral side lengths

• No, it's impossible

What would be the approximate side length of a regular octagon with an area of 10 units squared?

• 1.44

• 2.5

• 4.2

• 3.6

What does it mean for a polygon to have integral length sides?

• All sides are irrational numbers

• All angles are equal

• All sides are whole numbers

• All sides are equal