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!

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.

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°

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°

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

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= 1 2 6𝑚 72𝑚 𝑨𝒓𝒆𝒂 𝒐𝒇 𝒂 𝒑𝒐𝒍𝒚𝒈𝒐𝒏=𝟐𝟏𝟔 𝒎 𝟐

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 42.25+ 𝑥 2 =64 − 42.25 − 42.25 𝑥 2 =21.58 𝑥 2 = 21.58 𝒙≈𝟒.𝟔𝟒 𝟒.𝟔𝟒 𝟗.𝟐𝟖 𝑃𝑒𝑟𝑖𝑚𝑒𝑡𝑒𝑟=9.28 5 =46.4 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛= 1 2 𝑎𝑃 𝐴𝑟𝑒𝑎 𝑜𝑓 𝑎 𝑝𝑜𝑙𝑦𝑔𝑜𝑛= 1 2 6.5 46.4 𝑨𝒓𝒆𝒂 𝒐𝒇 𝒂 𝒑𝒐𝒍𝒚𝒈𝒐𝒏=𝟏𝟓𝟎.𝟖

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