Properties of Polygons and Triangles

This video tutorial explains how to calculate the area of regular polygons when only a side length is given. It covers the use of the formula involving the apothem and perimeter, and demonstrates how to find the apothem using trigonometry and special triangles like the 30-60-90 triangle. The tutorial includes example calculations and concludes with a summary of the methods discussed.

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

• Area = 1/2 × side length × perimeter

• Area = side length × perimeter

• Area = side length × apothem

• Area = 1/2 × apothem × perimeter

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CCSS.2.G.A.1

What is a regular polygon?

• A polygon with all sides equal but angles different

• A polygon with all angles equal but sides different

• A polygon with all sides and angles equal

• A polygon with no equal sides or angles

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CCSS.3.MD.D.8

How do you calculate the perimeter of a regular polygon with 6 sides, each of length 13?

• 13 - 6

• 13 ÷ 6

• 13 × 6

• 13 + 6

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CCSS.6.G.A.1

What is the next step after finding the perimeter in calculating the area of a regular polygon?

• Finding the apothem

• Finding the side length

• Finding the angle

• Finding the radius

What is the angle of each section in a regular hexagon?

• 90 degrees

• 30 degrees

• 45 degrees

• 60 degrees

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CCSS.HSG.CO.C.10

In a 30-60-90 triangle, what is the relationship between the hypotenuse and the shortest side?

• The hypotenuse is twice the shortest side

• The hypotenuse is three times the shortest side

• The hypotenuse is half the shortest side

• The hypotenuse is equal to the shortest side

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CCSS.8.G.B.8

What is the length of the hypotenuse if the shortest side of a 30-60-90 triangle is 6.5?

• 6.5

• 13

• 19.5

• 26

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CCSS.6.G.A.1

How do you treat a triangle when calculating the area as a regular polygon?

• As a circle

• As a regular polygon

• As a square

• As an irregular polygon

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CCSS.8.G.A.5

What is the sum of the interior angles of a triangle?

• 360 degrees

• 180 degrees

• 90 degrees

• 270 degrees

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CCSS.8.G.A.5

What is the angle of each section in an equilateral triangle?

• 90 degrees

• 60 degrees

• 30 degrees

• 45 degrees

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CCSS.8.G.A.5