Name: ___________________________________________ 14-1 NotesGeometry Pd. _____ Date: ____

Today’s Goal: How do we find the area of Regular Polygons?

Partner Discovery!Directions: Your team has been provided a regular polygon inscribed inside of a circle.

Your Task: Find the area of the regular polygon.

Initial Thoughts:

Use the following questions to assist your investigation:

1. Use your straight edge to draw in segments from the center of the circle to each vertex of the regular polygon (to each corner).

These segments are the of the circle and so they are all (relationship) .

2. What type of polygons have you cut your regular polygon into? (Hint: What do you know about its sides?)

3. What is the measure of each vertex angle of these triangles? [remember, which angles are base angles and which are vertex angles?]

4. Now sketch the angle bisector of at the vertex angle of one isosceles triangle. What is the measure of each smaller angle? _____________

In an isosceles triangle, the angle bisector is also the _____________ bisector. Mark the right angles and the two congruent pieces on your diagram.

Now you have created two _________________ triangles inside each isosceles triangle.

Mark and label your right triangle here:

5. Find the length of this perpendicular bisector to the nearest hundredth [Remember, you have a RIGHT triangle with a known angle and side- how do we find the missing side?]

Let’s come back together as a class!NEW VOCAB ALERT!The segment from the center of the circle to the base of the isosceles triangle has a special name!We call this segment/distance the:

Let’s try one!

Another One!

Round to the nearest 10th.

Find m∡ AFB Find m∡GFA

Find mGA Find mFG

First: calculate the apothem!

1. If not already there, draw in the Apothem (mark the right angles) and bisect the central angle to find the vertex angle of the small RIGHT triangle.

2. Bisect the base of the isosceles triangle to find the length of one side of the right triangle.

3. Use SOH CAH TOA to calculate the length of the apothem.

Second: Calculate the Area!

1. Find the area of each triangle2. Multiply the area by the # of triangles

in the regular polygon.

Name: _______________________ 14-1 Practice

Geometry Pd. ______ Date: _____

Complete each of the following problems. Show all your work!

1. Given regular polygon ABCDEFGKH.

Find a)m∠GJH b) m∠GJK

2. Calculate the Apothem for the regular polygon found below to the nearest 10th:

3. A regular hexagon has an apothem of 10 units.a. Find the radius of the hexagon and the length of one side.

b. Find the area of the hexagon.

4. Find the area of the shaded region.

Part A: Draw the triangles and Apothem and calculate the length of the apothem to the nearest 100th.

Part B: Calculate the area of the regular Polygon.

Part C: Calculate the area of the Circle to the nearest integer.. What other information do you need to find?

Part D: Subtract appropriate areas to find area of the shaded region.

Name: __________________________________ 14-1 HWGeometry Pd. _____ Date: ____

Directions: Complete each of the following problems. Show all work to earn credit.

1. Find the given angle measure for regular hexagon ABCDEF.

a) mCGD b) mCGH

2. Find the area of the regular polygon to the nearest 10th. Remember to find the apothem first!

3.

a) Calculate the arc length of arc QS. Leave in terms of Pi.

4. Find the circumference of circle N.

5. Error Analysis! Consider the student work below. Find the error he made AND correct it!

6. State the radius and center of the following circle. Graph the circle below.

radi