(1) Find the area of an equilateral triangle if each side is 8. F
· (2) Given the figure to the right with measures as marked, find: A B » , mÐ BAF , mÐ E
» , mAB mBC
100° E D 95° C 90° (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 10 3 . 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, uuur AB is tangent to the circle at B. FD is a diameter, with measures as marked. Find: 80° B C 6
G 1 A 2 20° F 3 P
· 40° H 65° 5 D » , mÐ 1 , » , mDE » , mEF mBG mÐ 2 , mÐ 3 , mÐ 4 , mÐ 5 , mÐ 6
4 E (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, W ABCD is a trapezoid with AB P CD and sides and angles as marked. Find the area and perimeter of W ABCD . A (9) Given the figure below, BC ^ AC , CD ^ AB , and sides as marked. Find: CD , BD and the area of V ABC B B 12 60° D 15 16 12 45° C D C A D (10) Given the figure to the right, W ABCD is a rhombus, with AF ^ BC . AC = 10 , BD = 24. Find: A E BC , area W ABCD , AF C F B (11) In a circle whose radius is 6, the area of a sector is 15p . 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 , DE = 23 , AB = BC. Find: AB (14) Given the figure below with sides and angles as marked. Find: DE and BE C 23 E D 9 B 7 A 18 E D 5 C A 8
B (15) In V ABC below, mÐ 1 = mÐ 2 , and sides are as marked. Find: BD and CD A (16) The length of each lateral edge in the cube below is 6. Find: the LSA, TSA volume , BD and BH. H 1 2 15 9 G E F D B C C D A B 16 uuur (17) AB is tangent to the circle below. Find AB given sides as marked. B (18) Find the area of the shaded region in the figure below if O is the center of the circle 120° A A C 4 D B 6 6
O 12 (19) A square pyramid with base edge 4 is inscribed in a cone with height 6. Find the volume of the pyramid and cone. (20) Find the volume of a sphere inscribed in a cube if each side of the cube is 6. (21) The area of an equilateral triangle is 25 3 . Find the length of its sides and altitudes please. (22) Solve for x in the circle below, given sides as marked. (23) W ABCD is a parallelogram, BD = 5 , DF = 4 , CF = 2. Find: DE and BE D 4 2 C x 8 E 6 A (24) The radius of the circle below is 20. The length of AB is 24. How far is AB from the center of the circle? A F 4 B (25) In the figure below, AC ^ BC , CD ^ AB , with sides as marked. Find: CD , AD , AC B 24 B 4 D 12 A (26) Given the figure below. BD ^ AC , AE ^ CE , with sides as marked. Find: AB , BC , BD C (27) Given the figure below, with sides and angles as marked, find: AE and AB D E 5
3 D 7 15 E 5 6 C A B 2 C A B (28) Find the sum of the areas of the shaded regions in the figure below given lengths and arcs as marked. (29) Find the LSA , TSA , and volume of the right regular hexagonal pyramid below if the altitude is 4 3 and each edge of the base is 6. B 6 8 C A 90° 90° D (30) Points P and Q are the centers of the circles in the figure below. PQ = 6. Find the area and perimeter of the shaded region. (31) W ABDE is a parallelogram in the figure below, with sides as marked. Find: a VABF aVCDF DE , CD , , aV CDF aW DEAB A A B 8 4 6 C P · · Q F
D E B (32) D ABC has vertices A ( -5 , 4) , B (1 ,
-2) and C (3 , 6). suur (a) Write the equation of AB . suur (b) Write the equation of the altitude to AC . (c) Write the equation of the perpendicular bisector of AC . (d) Find the perimeter of D ABC . (e) Find the length of the median to AB . 7 (33) D C A B 7 II I III IV
D C Given the figure above, AB P CD , sides as marked. Find the ratio of the areas of each of the following. A (34) 4 E 3 D 2 1 B F Given: AB = AC , DF ^ AB , EF ^ AC
Prove: BD g EF = CE g DF Answers (1) 16 3 » = 90 o , mÐ BAF = 45 o , mÐ E = 35 o » = 80 o , mAB (2) mBC C (3) Length of arc is 3p , area of sector is 15p (4) Each side is 20 , area of the hexagon is 600 3 (5) Volume is 400 , LSA is 260 , TSA is 360 » = 90 o , mÐ 1 = 20 o , » = 90 o , mDE » = 40 o , mEF (6) mBG mÐ 2 = 10 o , mÐ 3 = 45 o , mÐ 4 = 70 o , mÐ 5 = 45 o , mÐ 6 = 55 o (7) 12 (8) Area = 54 3 + 54 , perimeter = 30 + 6 6 + 6 3 (9) CD = 12 , BD = 9 , area = 150 (10) BC = 13 , area W ABCD = 120 , AF = 120 13 (11) Central angle is 150 o , arc length of the sector is 5p (12) Area inscribed circle is 12p , area circumscribed circle is 48p (13) AB = 12 (14) DE = 14 , BE = 15 3 2 (15) Interior angle is 172 o , exterior angle is 8 o (16) BD = 6 , CD = 10 (17) LSA = 144 , TSA = 216 , Volume = 216 , BD = 6 2 , BH = 6 3 (18) AB = 8 (19) 12p - 9 3
Answers (20) Volume pyramid = 32 , volume cone = 16p (21) 36p
(22) side = 10 , altitude = 5 3 (23) x = 3 (24) DE = 2 , BE = 3 (25) 16 (26) CD = 8 2 , AD = 32 , AC = 24 2 (27) AB = 40 , BC = 249 , BD = 75
17 17 17 (28) AE = 38 , AB = 54 5 5 (29) 25p - 49
(30) LSA = 90 3 , TSA = 144 3 , Volume = 216 (31) area = 48p + 18 3 , perimeter = 16p (32) DE = 8 , CD = 4 , a VABF 4 aVCDF 1 = , = aV CDF 1 aW DEAB 12 (33) (a) y = - x - 1
(b) y = - 4x + 2
(c) y = - 4x + 1
(d) 4 17 + 6 2 (e) 5 2