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Geometry Spring Final Review 4th Six Weeks: I. Complete the chart. MAKE SURE YOU KNOW THE FORMULAS FOR THE TEST! Type of Polygon Interior Angle Sum Measure of EACH Exterior Angle Sum Measure of EACH Interior Angle Exterior Angle 1. 150 2. 18 3. 1260 II. Quadrilaterals. Find the requested information. 4. Square with Perimeter of 80 5. Rectangle x A 5x y B z n° 3y+2 E 2z+10 x M Q d° 5x-9 b° 29 N e° A F a CF AB B 3a+1 m° CF p° 88 q° 4a+5 n° DE C m n 64 6a+2 E D p e PL q b° 9. Parallelogram PN L 28° a M N 6a-7 d x 90 a 58 55 46° ° 75 b c 17° e ° A Perimeter 3a-2 c° f° d° 4a+1 7. Trapezoid with midsegment mMNP 8. Kite P r mMNR P 2a+2 d q C c R n r° D a b m BC=12 CD=16 p° MN Perimeter c° a° p C DE 74 E n 6. Rhombus 3x-1 q° m p° AC B m° n° AD m° D A BD d D c b f 38 5y e C B 5x y BC CD Perimeter a b e c mLPN d e f III. More Polygons. 10. If the interior angle sum of a polygon is 1080 , what kind of polygon is it? IV. 11. If the exterior angle measure of a polygon is 30 , what is its exterior angle sum? Ratios and Proportions. 12. Solve for x. 13. The sides of a quadrilateral are in the ratio 2:3:5:6. The perimeter of the quadrilateral is 272 feet. Find the length of each side. 2x 1 5 3x 2 2 14. The interior angles of a triangle are in the ratio 2:3:5. Find the measure of each angle. V. Review Pythagorean Theorem, Special Right Triangles and Triples! This is 5-7 and 5-8 in your textbook. See page 365 and 369 for sample problems. 5th Six Weeks: I. Find the area of the following figures. REMEMBER… if you use a triple, write “TRIPLE.” 1. RHOMBUS. 2. KITE. 10 6 16 17 Perimeter = 68 inches 3. ISOSCELES TRIANGLE. 4. ISOSCELES TRAPEZOID. 11 13 12 5 5 5. PARALLELOGRAM. 6. RECTANGLE. 17 10 12 6 6 20 16 22 7. REGULAR HEXAGON. 8. CIRCLE. 18 Diameter = 12 II. SHOW YOUR WORK. Find the lateral area, total area, and volume for each figure. 9. Right Cone with Base of Area 108 square 10. Right Cylinder with Base Circumference = inches. meters LA = _________ B = __________ TA = _________ V = __________ 8 root 3 11. Regular Pyramid with Slant Height = 10 feet and Apothem = 6 feet LA = _________ B = __________ TA = _________ V = __________ LA = _________ B = __________ TA = _________ V = __________ 19 12. Regular Square Pyramid LA = _________ B = __________ TA = _________ V = __________ 12 inches 18 inches 13. Cube with an edge of 5. LA = _________ B = __________ TA = _________ V = __________ 14. Sphere with a diameter of 20 inches. LA = _________ B = __________ TA = _________ V = __________ 16 III. SHOW YOUR WORK. 15. Find the height of a right cylinder whose total area is 279 square meters and whose radius is 11 meters. 16. Find the total area of a cube whose volume is 64 cubic inches. 17. Find the radius of a sphere if the surface area of the sphere is 784 square inches. 18. Find the height of a right cone if its radius is feet and its lateral area is 544 square feet. 16 6th Six Weeks: I. Find the requested information. SHOW YOUR WORK. 1. Find the area of the sector (shaded). Leave your 2. Find the area of the circle segment (shaded). answer in terms of . Round your answer to the nearest tenth. 240 degrees 15 cm 9 in Asegment ____________ Asector ____________ » . Round your answer 3. Find the LENGTH of CD to the nearest hundredth. OP and MP are tangents to e N . O 9 192 degrees C 5x-3 D y _____ PN _____ 4y LCD » ____________ 5. x ______ N 6 P 7 ft M OP _____ 6. S C 60 82 T x ______ B G » ______ mAB 8. 129 » ______ mGC D mABC ______ B ј mSUR ______ 7. 79 A x ______ ј mTSU ______ y U (15x) y ______ R x 39 x ______ x A 4. 145 A B 26 34 D C C x E x ______ » ______ mDE 9. DG and FG are tangents of E . x ______ D » ______ mDF C E x 10. 70 J x ј mDCF ______ 52 G mKLH ______ 87 L mDCF ______ F H 78 I 11. x ______ Q 12. mWVT ______ U y ______ y » ______ mUV mNPO ______ N P x ______ є ______ mJI K (3x+5) W » ______ mNO 36 76 (5x-9) V O R 13. AY ______ T 14. AC ______ 279 8 C2 m» AB ______ Z mIBH ______ 5x-3 A AB ______ B Y x ______ I B H J 260 » ______ mHI G 22 100 mAYZ ______ A II. 15. Find the requested trigonometric ratios using the given right triangle. 16. B 5 3 sin C cos B cos C tan B tan C C A III. sin B E 15 8 D sin D sin F cos D cos F tan D tan F F Draw and label a right triangle. Then find the requested ratio. 17. If sin C 7 , then find cos C . 25 18. If tan B 12 , then find sin B . 5 IV. Solve for the variable(s). Round lengths to the nearest tenth and angles to the nearest degree. Be sure to give your equation in calculator-ready form BEFORE you get your answer. 20. 21. 19. x 16 V. 22. 20 42 x 10 64° x 17 Solve each triangle. Round lengths to the nearest tenth and angles to the nearest degree. 23. 24. F m g B p F C M f M A B 73° G a 30 25 21 g 15 f a C 61° p P m N H VI. WORD PROBLEMS. 25. Find the angle of elevation if a 45-foot flagpole casts a shadow 63 feet long. Answer to the nearest degree. 26. An observer on the ground is 1.5 miles from a building that is 1600 feet tall. What is the angle of depression from the building to the observer? 27. A kite is flying at an angle of elevation of about 62 degrees. The entire length of the string has been let out. The height of the kite above the ground is 40 meters. How much string has been let out? 28. A certain jet is capable of a steady 16 degree climb. How much altitude does the jet gain when it moves 1 kilometer through the air? Answer to the nearest 50 meters.