Understanding Regular Polygons and Triangles

This video tutorial continues with the area of regular polygons worksheet, focusing on using special right triangles to find the area of various polygons. The instructor explains the properties of 30-60-90 and 45-45-90 triangles and applies these to calculate the area of triangles and hexagons. The video covers solving for the apothem and perimeter, using ratios, and simplifying expressions to find the area in simplest form.

What is the main focus of the worksheet discussed in the video?

• Learning about irregular polygons

• Identifying different types of polygons

• Calculating the area of regular polygons

• Finding the perimeter of polygons

Which special right triangle has side ratios of 1, √3, and 2?

• 90-90-90 triangle

• 45-45-90 triangle

• 30-60-90 triangle

• 60-60-60 triangle

In a 45-45-90 triangle, what is the ratio of the sides?

• 1:√3:2

• 1:1:1

• 1:1:√2

• 1:2:√3

What is the first step in finding the area of a regular triangle using a 30-60-90 triangle?

• Calculate the perimeter

• Identify the apothem

• Determine the side ratios

• Find the hypotenuse

If the length of one side of a regular triangle is 18, what is the length of the apothem?

• 9

• 18

• 36

• 27

How do you calculate the perimeter of a regular triangle?

• Multiply the side length by 2

• Multiply the side length by 3

• Add all side lengths

• Divide the side length by 3

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

• Base × height

• 1/2 × apothem × perimeter

• 1/2 × base × height

• Apothem × perimeter

In the hexagon problem, what is the given apothem?

• 8√3

• 8

• 4

• 4√3

How many sides does a hexagon have?

• 4

• 5

• 6

• 8

What is the perimeter of a hexagon if one side is 8?

• 24

• 32

• 40

• 48