GEOMETRY AREA UNIT. Day I Area Review. Triangle Parallelogram Rectangle. A b h. Square Trapezoid Kite. b 2. b 1. 1 Atrapezoid h b1 b2

Transcription

1 GEOMETRY RE UNIT Day I Review Objectives: SWBT fid the area of various shapes Triagle Parallelogram Rectagle triagle base height b h parallelog ram base height b h recta gle base height b h Square Trapezoid Kite b d square square side s b height base base trapezoid hb b trapezoid d diagoal diagoal Kite d d Kite

2 Rhombus Circle Sector diagoal diagoal r hombus d d r hombus circle circle radius r sector Cetral N sector r radius Fid the area of the followig shapes recta gle ft b h square 3 s triagle b h 9 i uits

3 hb b Need Height trapezoid Use Pythags 3 h 5 9 h 5 trapezoid trapezoid h 6 h 4 trapezoid hb b trapezoid 40 6 trapezoid i b h parallelog ram 8 5 parallelog ram parallelog ram 0 cm d d d 4 r hombus d 0 r hombus 4 r hombus r hombus 4 uits

4 hb b Need Height trapezoid Use Pythags h 50 h 50 trapezoid trapezoid h 49 h 7 trapezoid hb b trapezoid 7 trapezoid cm Hypo Small 0 b 5 Small Middle / Log 5 3 h 5 3 triagle b h ta C Opposite djacet 7 ta8 b ta8 7 b Cross Multiply b ta 8 7 b b mm or 56.9 mm recta gle b h i

5 cm Hypo Leg 3 s 3 square 3 s 9 i N sector r 90 sector 4 90 sector 96 sector mm sector N sector r 0 sector 7 0 sector 49 sector sector cm 3

6 Day II of Figures Objectives: SWBT fid the area of various shapes ad shaded regios of a Figure: If you kow the shape of the shaded area just use the formula If it is t a shape you recogize the thik of it as BIG SHPE LITTLE SHPE Space Big Small Ibetwee Shape Shape Examples: Fid the area of the shaded area... Space Big Small Ibetwee Shape Shape Rectagle-Rectagle h b h b i Space Big Small Ibetwee Shape Shape Circle-Rectagle r h b i

7 cm Diameter radius 6 r r 8 Space Big Small Ibetwee Shape Shape Square-Circle s r i hb b Need the Height 5 h 5 Trapezoid 5 h 50 h 5 h cm

8 5. 6. Space Big Small Ibetwee Shape Shape Space Big Small Ibetwee Shape Shape Square 4Rectagles Rectagle Triagles s 4 h b h b h b cm 464 ft

9 Day III of Compoud Figures Objectives: SWBT fid the area of various shapes of a Compoud Figures or Ufamiliar Shapes: Break it up ito shapes that you kow the DD UP THE SHPES ONLY DRW Straight Lies Examples: Fid the area of the give shapes... Total Rectagle Rectagle Total h b hb Total 684 Total 3 Total 44 cm Total Rectagle Rectagle Total h b hb Total 3558 Total 5 40 Total 45 ft

10 3. 4. Triagle Need Base 8 b 0 64 b 00 b 36 b 6 Total Rectagle Triagle Total h b h b Total Total 98 4 Total cm Total Rectagle Trapazoid Total h b hb b Total Total 4 80 Total 94 cm

11 5. 6. Total Trapezoid Triagle+Rectagle Total h b Total Total b hb h b Total 4 i Diameter radius 0 r r 5 Total Trapezoid Rectagle+Half Circle Total h Total Total b b h b r 0 Total. 5 cm

12 Regular Polygos: Day IV of Regular Polygos Day Polygos with cogruet sides ad agles pothem: segmet from the ceter that is a Perpedicular Bisector of a side Radius: segmet from the ceter that bisects agle of the polygo Perimeter: Objectives: SWBT fid the area of regular polygos dd up all the side or multiply the umber of sides ad the legth of a Regular Polygo Formula: apothem Perimeter ap Examples: Fid the area of the followig regular polygos.. 3. ap Perimeter ap Perimeter ap Perimeter i 9. i 3 ft

13 ft ap Perimeter ap Perimeter i 9 3 or i i 6. Need pothem 3 a 6 9 a 36 a 7 a 3 3 ap Perimeter Need Side Give Half Side Side 33 Side i or i

14 Day V of Regular Polygos Day Objectives: SWBT fid the area of regular polygos usig Special Right Triagles of a Regular Polygo Formula: apothem Perimeter ap Cetral gle: agle made by two radii Radius: segmet from the ceter that bisects agle of the polygo Side: Half Side: Half of the side of a petago Steps for Fidig the of a Regular Polygo Fid Cetral gle Cetral Divide the Cetral gle i Half to fid the top agle i your triagle Cetral Top i Triagle Radius Hypoteuse 3 - sk yourself what you have ad label your Triagle Do I have a radius/hypo? Do I have the apothem? Do I have a side? Whatever it is, label your triagle! x side 4 Fid out what you eed to complete the formula. If you eed the apothem or a, use SOH-CH-TO / a b c If you eed side or x, use SOH-CH-TO / a b c apothem 5 Fid the Perimeter Oce you have x, double it ad multiply that by the umber of sides 6 Iput all data ito the formula ap

15 Examples: Fid the area of the followig regular polygos. Cetral Cetral 6 Cetral60 4 ta 30 a ta 30 4 a a ta 30 4 a ta 30 a Need pothem Half Side 4 Side 8 ap Perimeter i. Cetral Cetral 6 Cetral60 Need Half Side pothem 6 ap Perimeter x ta 30 6 ta 30 x 6 6 ta 30 x x 6 ta 30 x Side i

16 3. x si 30 si 30 x si 30 x 6 x x si 30 a cos30 cos30 a cos 30 a cos 30 a 0.39 a Cetral Cetral 6 Cetral60 Need Half Side Need pothem Radius Side ap Perimeter mm 4. Cetral Cetral 6 Cetral60 6 ta 30 a ta 30 6 a a ta a ta 30 a 0.39 Need pothem Side Half Side 6 ap Perimeter ft

17 5. Cetral Cetral 3 Cetral0 Need Half Side pothem 6 x ta 60 ta 60 x ta 60 x ta x x 60 ap Perimeter ft Side 6.98

18 Day VI of Regular Polygos Day 3 Objectives: SWBT fid the area of regular polygos give oly piece of data Examples: Fid the area of the followig regular polygos. Need Half Side Need pothem Radius 3 Cetral Cetral 6 Cetral60 x si 30 3 si 30 x 3 3si 30 x 3si 30 x.5 Side 3 x a cos30 3 cos30 a 3 3cos 30 a 3 cos 30 a. 598 a ap Perimeter cm

19 . Cetral Cetral 5 Cetral7 Need Half Side pothem ap Perimetr e x ta 36 ta 36 ta 36 x ta 36 x.453 x ft Side.906 Cetral Cetral 8 Cetral45 Need Half Side Need pothem Radius 6 x si.5 6 si.5 x 6 6 si.5 x x 6 si.5 x.96 Side a cos.5 6 cos.5 a 6 6 cos.5 a 6 cos.5 a a ap Perimeter ft

20 4. Cetral Cetral 8 Cetral45 5 ta. 5 a ta.5 5 a a ta.5 5 a ta 5.5 a.07 Need pothem Side 0 Half Side 5 ap Perimeter i

21 Day VII gles of Regular Polygos Objectives: SWBT fid the area of regular polygos Regular Polygos: If it is equiagular ad equilateral ll sides ad agles are cogruet Sum of Iteral gles Formula of a Polygo Sum 80 Number of Sides Fid the value of x Sum 80 6 Sum x x x x x x x 70 x 0 Sum 80 4 Sum 80 5 Sum Sum x x x80 36x 4x 80 x 45 x x x x x x 370 x 37

22 Sum of Iteral gles Formula of a Regular Polygo Sum 80 Number of Sides 80 gle For Re gular Polygos Oly Give the followig regular polygos, fid the sum of the iterior agles. 4. Hexago 5. Noago 6. Octago Sum 80 6 Sum Sum Sum Sum Sum You are give the measure of each iterior agle of a regular -go. Fid the umber of sides m m m Cross Mulitply Cross Mulitply Cross Mulitply

23 Sum of Exteral gles Formula of a Regular Polygo Exteral gles add up degrees Solve for x x 6x 9x 7x 39 7x x 3 x x x x x x 0 8x x 0 Give the followig regular polygos, fid the umber of degrees of each exterior agle go 0. Petago. Heptago 6x x 60 5x x 7 7x x 5.43