1. Today – Friday, June 7, 2013
Learning Target : You will find area of regular polygons inscribed in a circle.
Independent practice
BRING BOOKS ALL NEXT WEEK!

2. Some important VOCABULARY:
CENTER OF THE POLYGON: exact middle of a figure.
RADIUS OF A POLYGON (CIRCLE): distance from the center of the figure to a vertex.
APOTHEM OF A POLYGON: Height to the base of an isosceles triangle that has two radii as it’s legs.
CENTRAL ANGLE OF A REGULAR POLYGON: Angle formed that connects two consecutive vertices of a regular polygon.

3. PRACTICE: To find the measure of the central angle, use the formula 360° 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑠𝑖𝑑𝑒𝑠 .
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒= 360° 6
𝒄𝒆𝒏𝒕𝒓𝒂𝒍 𝒂𝒏𝒈𝒍𝒆=𝟔𝟎°
𝑐𝑒𝑛𝑡𝑟𝑎𝑙 𝑎𝑛𝑔𝑙𝑒= 360° 4
𝒄𝒆𝒏𝒕𝒓𝒂𝒍 𝒂𝒏𝒈𝒍𝒆=𝟗𝟎°

4. PRACTICE: In the diagram 𝐴𝐵𝐶𝐷𝐸𝐹 is a regular polygon inscribed in ʘ𝐹
PRACTICE: In the diagram 𝐴𝐵𝐶𝐷𝐸𝐹 is a regular polygon inscribed in ʘ𝐹. Find each angle measure.
∠𝐴𝐹𝐵is a central angle so
𝑚∠𝐴𝐹𝐵= 360° 5
𝒎∠𝑨𝑭𝑩=𝟕𝟐°
∠𝐴𝐹𝐺is half the central angle so
1 2 𝑚∠𝐴𝐹𝐵= 1 2 ∙ 360° 5
𝒎∠𝑨𝑭𝑮=𝟑𝟔°
Use the triangle sum theorem:
36°+90°+𝑚∠𝐺𝐴𝐹=180°
126°+𝑚∠𝐺𝐴𝐹=180°
𝒎∠𝑮𝑨𝑭=𝟓𝟒°

5. AREA OF A REGULAR POLYGON: The area of a regular n-gon with side lengths s is half the product of the apothem a and the perimeter p.
𝑨𝒓𝒆𝒂= 𝟏 𝟐 𝒂𝑷 𝑎 𝑠

6. PRACTICE: Find the area of the regular polygon.
12𝑚 6𝑚
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=12𝑚 6 𝑠𝑖𝑑𝑒𝑠 =72𝑚
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛= 1 2 𝑎𝑃
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛= 𝑚 72𝑚
𝑨𝒓𝒆𝒂 𝒐𝒇 𝒂 𝒑𝒐𝒍𝒚𝒈𝒐𝒏=𝟐𝟏𝟔 𝒎 𝟐

7. PRACTICE: Find the length of a side in the regular pentagon using Pythagorean theorem. Then find the perimeter and area of the figure.
Find leg of right triangle using Pythagorean Theorem:
𝑙𝑒𝑔 2 + 𝑙𝑒𝑔 2 = ℎ𝑦𝑝 2
(6.5) 2 + 𝑥 2 = 8 2
𝑥 2 =64
− − 42.25
𝑥 2 =21.58
𝑥 2 =
𝒙≈𝟒.𝟔𝟒
𝟒.𝟔𝟒
𝟗.𝟐𝟖
𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟= =46.4
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛= 1 2 𝑎𝑃
𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛=
𝑨𝒓𝒆𝒂 𝒐𝒇 𝒂 𝒑𝒐𝒍𝒚𝒈𝒐𝒏=𝟏𝟓𝟎.𝟖

8. HOMEWORK #4:
Pg. 765: 1-13, 15-16
If finished, work on other assignments:
HW #1: Pg. 723: 3-8, 16-18, 22-24
Pg. 733: 3-5, 10-12, 19-21
HW #2: Pg. 749: 3-7, 11-13, 15-23
HW #3: Pg. 758: 7-9, 11-16, 27-29