Polygon Area

Polygon Area & Angles

Dr. Tom Giles​

S

Angles & Areas of Polygons

Learning Target: I can calculate angle measures and the area of polygons.

What can we calculate?

• Exterior Angle Sum

• One Exterior Angle

• Interior Angle Sum

• One Interior Angle

• Central Angle

• Area of a Polygon

Multiple Choice

Which option shows the formula to solve for a polygon's angle sum?

• $$180n$$

• $$180\left(n-2\right)$$

• $$\left(180-2\right)n$$

• $$\frac{180\left(n-2\right)}{n}$$

Multiple Choice

What is the SUM of the angle measures in a nonagon (9 sides)?

• 1440°

• 900°

• 1080°

• 1260°

Multiple Choice

Find the value of X. (Use your knowledge of angle sum to set up an equation and solve.)

• 100

• 120

• 125

• 130

One interior angle

• If we can solve for the angle sum, we can also find one angle

• This works for regular polygons

Multiple Select

What is a regular polygon? (choose all that apply)

• all side lengths are the same length

• only some angles are the same

• only some side lengths are the same

• all side lengths are different

• all angles are the same (equal in measure)

One interior Angle

• Find the angle sum using the formula

• Divide by the number of angles (the same as the number of sides)

Multiple Choice

Which option shows the formula to solve for ONE interior angle of a polygon?

• $$180n$$

• $$180\left(n-2\right)$$

• $$\left(180-2\right)n$$

• $$\frac{180\left(n-2\right)}{n}$$

Multiple Choice

Find the measure of one interior angle of this regular nonagon. Round your answer to the nearest tenth if necessary.

• A

• B

• C

• D

Multiple Choice

Find the measure of one interior angle in the regular 11-gon. Round your answer to the nearest tenth if necessary.

• A

• B

• C

• D

Multiple Choice

Find the measure of one interior angle in the regular pentagon. Round your answer to the nearest tenth if necessary.

• A

• B

• C

• D

Determining Area of Polygons

• Step 1 : split your polygon into triangles

• Step 2: Find one angle (interior or central)

• Step 3: Use trig to find missing side(s)

• Step 4: Find area of the triangle

• Step 5: Multiply by the number of triangles

Multiple Choice

What would be the first step in finding the area of the pentagon?

• draw in traingles

• calculate the length of the side

• calculate the length of the radius

• find the angle measure

Fill in the Blanks

How many triangles does this create?

Multiple Choice

What would be the next step in finding the area of the pentagon?

• draw in the apothem

• calculate the length of the side

• calculate the length of the radius

• find the angle measure

Fill in the Blanks

What is the measure of the angle you found?

Multiple Choice

What method do you use to solve for the missing sides?

• Pythagorean Theorem

• Addition

• Trig

Open Ended

The next step is finding the missing side lengths. Write your side lengths below.

Fill in the Blanks

What is the area of your triangle to the nearest whole number?

Multiple Choice

What is the last step in solving for the area of the polygon?

• Find the perimeter.

• Multiply by the number of triangles.

• Nothing, you're done.

Open Ended

What is your final area?