Geometry Final Exam Review Worksheet

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1 Geometry Final xam Review Worksheet (1) Find the area of an equilateral triangle if each side is 8. (2) Given the figure to the right, is tangent at, sides as marked, find the values of x, y, and z please. x y 8 z (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 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, LS and TS of the pyramid please. () Given the figure to the right, is tangent to the circle at. F is a diameter, with measures as marked. Find: 1 2 F G 20 3 P 80 5 H 5 40 mg, mf, m, m 1, m 2, m 3, m 4, m 5, m 4 (7) The areas of two similar triangles are 144 and 25. If a side of the smaller triangle is 9, how long is the corresponding side of the larger triangle?

2 Geometry Final xam Review Worksheet (8) Given the figure below, (9) Given the figure below,, is a trapezoid with and sides, and sides as marked. Find: and angles as marked. Find the area, and the area of and perimeter of (10) Given the figure to the right, is a rhombus, with F. = 10, = 24. Find:, area, F F (11) In a circle whose radius is, the area of a sector is 15 π. Find the measure of the central angle of the sector and the length of the arc of the sector please. (12) ach side of an equilateral triangle is 12. Find the area of its inscribed and circumscribed circles. (13) Given the figure below, = 9, (14) Given the figure below with sides and = 23, =. Find: angles as marked. Find: and

3 Geometry Final xam Review Worksheet (15) In below, m 1 = m 2, and sides are as marked. Find: and (1) The length of each lateral edge in the cube below is. Find: the LS, TS volume, and H H F G 1 (17) is tangent to the circle below. Find given sides as marked. (18) Find the area of the shaded region in the figure below if O is the center of the circle O (19) square pyramid with base edge 4 is (20) Find the volume of a sphere inscribed inscribed in a cone with height. Find the in a cube if each side of the cube is. volume of the pyramid and cone.

4 Geometry Final xam Review Worksheet (21) The area of an equilateral triangle is Find the length of its sides and altitudes please. (22) Solve for x in the circle below, given (23) is a parallelogram, = 5, sides as marked. F = 4, F = 2. Find: and 8 4 x 4 F 2 (24) The radius of the circle below is 20. The (25) In the figure below,, length of is 24. How far is from, with sides as marked. the center of the circle? Find:,, (2) Given the figure below., (27) Given the figure below, with sides and, with sides as marked. angles as marked, find: and Find:,,

5 Geometry Final xam Review Worksheet (28) Find the sum of the areas of the shaded (29) Find the LS, TS, and volume of regions in the figure below given lengths the right regular hexagonal pyramid and arcs as marked. below if the altitude is 4 3 and each edge of the base is (31) is a parallelogram in the figure below, with sides as marked. Find:,, a F a F, a F a 8 F 4 (32) has vertices ( 5, 4), (1, 2) and (3, ). (a) Write the equation of. (b) Write the equation of the altitude to. (c) Write the equation of the perpendicular bisector of. (d) Find the perimeter of.

6 Geometry Final xam Review Worksheet (e) Find the length of the median to. (33) 9 1 (34) 10 F I 7 II IV III 11 G Given the figure above, G, and F are midpoints. Find: G,, G, G, F, F Given the figure above,, sides as marked. Find the ratio of the areas of each of the following. a I a II, a I a III, a II a IV, a II a (35) F Given: =, F, F Prove: i F = i F

7 Geometry Final xam Review Worksheet nswers (1) 1 3 (2) x = 4, y = 3, z = 13 2 (3) Length of arc is 3π, area of sector is 15π (4) ach side is 20, area of the hexagon is 00 3 (5) Volume is 400, LS is 20, TS is 30 () mg = 40, mf = 90, m = 90, m 1 = 20, m 2 = 10, m 3 = 45, m 4 = 70, m 5 = 45, m = 55 (7) 12

8 Geometry Final xam Review Worksheet nswers (8) rea = , perimeter = (9) = 12, = 9, area = 150 (10) = 13, area = 120, F = (11) entral angle is 150, arc length of the sector is 5π (12) rea inscribed circle is 12π, area circumscribed circle is 48π (13) = 12 (14) = 14 3, = 15 2

9 Geometry Final xam Review Worksheet nswers (15) =, = 10 (1) LS = 144, TS = 21, Volume = 21, = 2, H = 3 (17) = 8 (18) 12 π 9 3 (19) Volume pyramid = 32, volume cone = 1π (20) 3π (21) side = 10, altitude = 5 3

10 Geometry Final xam Review Worksheet nswers (22) x = 3 (23) = 2, = 3 (24) 1 (25) = 8 2, = 32, = 24 2 (2) = 40 17, = , = (27) = 38 5, = 54 5

11 Geometry Final xam Review Worksheet nswers (28) 25 π 49 (29) LS = 90 3, TS = 144 3, Volume = 21 (30) area = 48 π , perimeter = 1π (31) = 8, = 4, a F a F = 4 1, a F a = 1 12 (32) (a) y = x 1 (b) y = 4x + 2 (c) y = 4x + 1

12 (d) (e) 5 2 Geometry Final xam Review Worksheet nswers (33) G = 15, = 15 2, G = 12, G =, F = 8, F = 10 (34) a I 11 = a II 7, a I 1 = a III 1, a II 49 = a IV 121, a II 49 = a 324

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