ࡱ> fheep -bjbjcTcT *>>fd[[313131G1G1G181,2G13];s;s;a<DDD"$$$$$$w$31DDDD$[[s;a<19D.[s;31a<"D"(La<cGG1rdO0 31|DDDDDDD$$ DDDDDDDDDDDDDDDD !:  (1) Find the area of an equilateral triangle if each side is 8.   (2)  (3) Find the length of the arc of a sector of 54( in a circle if the radius is 10. Find the area of the sector.  (4) The apothem of a regular hexagon is  EMBED Equation.DSMT4 . Find the length of each side of the hexagon. Find the area of the hexagon.   (5) The altitude of a regular pyramid with a square base is 12, and the slant height is 13. Find the volume, LSA and TSA of the pyramid please.  (6) Given the figure to the right,  EMBED Equation.DSMT4  is tangent to the circle at B.  EMBED Equation.DSMT4  is a diameter, with measures as marked. Find:  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4   (7) The areas of two similar triangles are 144 and 256. If a side of the smaller triangle is 9, how long is the corresponding side of the larger triangle? (8) Given the figure below,  EMBED Equation.DSMT4  (9) Given the figure below,  EMBED Equation.DSMT4  , is a trapezoid with  EMBED Equation.DSMT4  and sides  EMBED Equation.DSMT4  , and sides as marked. Find:  and angles as marked. Find the area CD , BD and the area of  EMBED Equation.DSMT4  and perimeter of  EMBED Equation.DSMT4 .   (10) Given the figure to the right,  EMBED Equation.DSMT4  is a rhombus, with  EMBED Equation.DSMT4 . AC = 10 , BD = 24. Find: BC , area  EMBED Equation.DSMT4 , AF  (11) In a circle whose radius is 6, the area of a sector is  EMBED Equation.DSMT4  Find the measure of the central angle of the sector and the length of the arc of the sector please.  (12) Each side of an equilateral triangle is 12. Find the area of its inscribed and circumscribed circles.  (13) Given the figure below, AD = 9 , (14) Given the figure below with sides and  DE = 23 , AB = BC. Find: AB angles as marked. Find: DE and BE  (15) In  EMBED Equation.DSMT4  below,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  , and (16) The length of each lateral edge in the  sides are as marked. Find: BD and CD cube below is 6. Find: the LSA, TSA volume , BD and BH.   (17)  EMBED Equation.DSMT4 is tangent to the circle below. Find AB (18) Find the area of the shaded region in the  given sides as marked. figure below if O is the center of the circle  (19) A square pyramid with base edge 4 is (20) Find the volume of a sphere inscribed inscribed in a cone with height 6. Find the in a cube if each side of the cube is 6. volume of the pyramid and cone.   (21) The area of an equilateral triangle is  EMBED Equation.DSMT4 . Find the length of its sides and altitudes please.  (22) Solve for x in the circle below, given (23)  EMBED Equation.DSMT4 is a parallelogram, BD = 5 , sides as marked. DF = 4 , CF = 2.  Find: DE and BE   (24) The radius of the circle below is 20. The (25) In the figure below,  EMBED Equation.DSMT4  , length of  EMBED Equation.DSMT4  is 24. How far is  EMBED Equation.DSMT4  from  EMBED Equation.DSMT4  , with sides as marked. the center of the circle? Find: CD , AD , AC   (26) Given the figure below.  EMBED Equation.DSMT4  , (27) Given the figure below, with sides and  EMBED Equation.DSMT4  , with sides as marked. angles as marked, find: AE and AB  Find: AB , BC , BD  (28) Find the sum of the areas of the shaded (29) Find the LSA , TSA , and volume of regions in the figure below given lengths the right regular hexagonal pyramid  and arcs as marked. below if the altitude is  EMBED Equation.DSMT4  and each edge of the base is 6.   (30) Points P and Q are the centers of the circles (31)  EMBED Equation.DSMT4 is a parallelogram in the figure in the figure below. PQ = 6. Find the below, with sides as marked. Find: area and perimeter of the shaded region. DE , CD ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4    (32)  EMBED Equation.DSMT4  has vertices A ( (5 , 4) , B (1 , (2) and C (3 , 6). (a) Write the equation of  EMBED Equation.DSMT4 . (b) Write the equation of the altitude to  EMBED Equation.DSMT4 . (c) Write the equation of the perpendicular bisector of  EMBED Equation.DSMT4 . (d) Find the perimeter of  EMBED Equation.DSMT4 . (e) Find the length of the median to  EMBED Equation.DSMT4 .  (33) (34)    (35) (36)  Answers (1)  EMBED Equation.DSMT4  (2)  EMBED Equation.DSMT4  (3) Length of arc is  EMBED Equation.DSMT4  , area of sector is  EMBED Equation.DSMT4  (4) Each side is 20 , area of the hexagon is  EMBED Equation.DSMT4  (5) Volume is 400 , LSA is 260 , TSA is 360 (6)  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  (7) 12 Answers (8) Area =  EMBED Equation.DSMT4  , perimeter =  EMBED Equation.DSMT4  (9) CD = 12 , BD = 9 , area = 150 (10) BC = 13 , area  EMBED Equation.DSMT4  = 120 , AF =  EMBED Equation.DSMT4  (11) Central angle is  EMBED Equation.DSMT4 , arc length of the sector is  EMBED Equation.DSMT4  (12) Area inscribed circle is  EMBED Equation.DSMT4  , area circumscribed circle is  EMBED Equation.DSMT4  (13) AB = 12 (14) DE =  EMBED Equation.DSMT4  , BE =  EMBED Equation.DSMT4  Answers (15) BD = 6 , CD = 10 (16) LSA = 144 , TSA = 216 , Volume = 216 , BD =  EMBED Equation.DSMT4  , BH =  EMBED Equation.DSMT4  (17) AB = 8 (18)  EMBED Equation.DSMT4  (19) Volume pyramid = 32 , volume cone =  EMBED Equation.DSMT4  (20)  EMBED Equation.DSMT4  (21) side = 10 , altitude =  EMBED Equation.DSMT4  Answers (22) x = 3 (23) DE = 2 , BE = 3 (24) 16 (25) CD =  EMBED Equation.DSMT4  , AD = 32 , AC =  EMBED Equation.DSMT4  (26) AB =  EMBED Equation.DSMT4  , BC =  EMBED Equation.DSMT4  , BD =  EMBED Equation.DSMT4  (27) AE =  EMBED Equation.DSMT4  , AB =  EMBED Equation.DSMT4  Answers (28)  EMBED Equation.DSMT4  (29) LSA =  EMBED Equation.DSMT4  , TSA =  EMBED Equation.DSMT4  , Volume = 216 (30) area =  EMBED Equation.DSMT4  , perimeter =  EMBED Equation.DSMT4  (31) DE = 8 , CD = 4 ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  =  EMBED Equation.DSMT4  (32) (a)  EMBED Equation.DSMT4  (b)  EMBED Equation.DSMT4  (c)  EMBED Equation.DSMT4  (d)  EMBED Equation.DSMT4  (e)  EMBED Equation.DSMT4  Answers (33) AG = 15 , BD =  EMBED Equation.DSMT4  , BG = 12 , EG = 6 , EF = 8 , BF = 10 (34)  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4      Geo 9 Geometry Exam Review Worksheet  PAGE 1  EMBED Equation.DSMT4  z y x 5 6 6 8 Given the figure to the right,  EMBED Equation.DSMT4  is tangent at B, sides as marked, find the values of x , y , and z please. P ( H G F E D C B A 80( 20( 40( 5 4 3 2 1 65( 12 12 6 60( 45( D C B A D C B A 16 15 F E D C B A 23 9 E D C B A 8 7 5 18 E D C B A 15 9 16 2 1 D C B A H G F E D C B A 12 4 D C B A 6 6 120( O B A x 6 8 4 2 4 F E D C B A 24 B A 12 4 D C B A 15 3 5 E D C B A 5 7 6 2 E D C B A 8 6 90( 90( D C B A ( ( P Q D C B A F E D C B A 4 8 6 8 9 10 6 7 5 G 4 3 2 1 F E D Given:  EMBED Equation.DSMT4  , Prove:  EMBED Equation.DSMT4  Given the figure above,  EMBED Equation.DSMT4 , sides as marked. Find the ratio of the areas of each of the following.  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  ,  EMBED Equation.DSMT4  11 7 E D C B A II IV III I Given the figure above,  EMBED Equation.DSMT4 , D and F are midpoints. 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