GEOMETRY REVIEW PROBLEMS, Spring 2018
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1 GEOMETRY REVIEW PROBLEMS, Spring 2018 Solve problems, describe problems algebraically, and simplify numerical expressions. 1. R(-3, -2), M(-1, -8) 2. R(11, -5), M(4, -4) 3. A(5, -4), B(-45, 20) 4. A(-10, 15), B(22, -17) 5. Find the value of the variable x 6. Find the value of the variable x 7. Diagonals of the rhombus PQRT intersect at the point T. Measure of the angle TPS s 30. Length of side TR equals 6 units. Find the length of the side QT (the exact algebraic expression and the decimal rounded to nearest hundredth). 1
2 8. Diagonals of the square DEFG intersect at H. Find the length of the side DE 9. Determine the value of each segment on the picture: BC = FC = GB = 10. 2
3 11. Two pentagons are similar. The area of the smaller pentagon is 75 ft 2. Find the area of the bigger pentagon. 12. Find the area of the polygon 13. Find lengths of diagonals in the rectangle 14. Find the length of the segment x 3
4 15. Find the length of the segment x 16. What is the area of the shaded region? 17. Find the surface area of the regular pyramid 4
5 18. Area of the isosceles right triangle is 400 yd 2. Find the length of the hypotenuse. 19. Find the height of the cylinder if the surface area is 325 m Estimate the height of the prism with the given surface area 6372 m The hypotenuse length of the isosceles right triangle is 30 ft. Find the area of such triangle. 22. Find the volume of the solid 5
6 23. Find the area of the base of the prism For problems 24 and 25 use the picture of the parallelogram below 24. Find the measure of the angle y 25. Find the measure of the angle x For problems 26 and 27 use the picture of the parallelogram below 26. Find the value of p. 6
7 27. Find the value of q. 28. Find the length of the diagonal in the parallelepiped with sides 12 in, 6 in, and 4 in. 29. Find the volume of the pyramid 30. Find the volume of the compound figure. Round your answer to the nearest whole number. 31. Find the area of the smaller trapezoid 7
8 32. Are two figures similar? For the problems 33 use the figure below 33. Find the perimeter of the equilateral triangle. 34. Find the surface area of the smaller figure if the surface area of the bigger figure is 96π and the scale factor is 1 : Find the volume of the bigger figure if the volume of the smalle figure is 25 m 3 and the scale factor is s = 3: 8
9 36. Find the volume of the cone: 37. Find the length of the diagonal PQ in the parallelepiped if SR = 5 in, RQ = 8 in, and QT = 4 in. P S T R Q 38. Find the lateral area of the cone: 39. Find the length of the arc in terms of π: 9
10 40. For the right triangle below find the value of the variable x 41. For the right triangle above find the value of the variable y. For problems 42 and 43 use the figure below 42. Find the side x. 43. Find the side y. 44. What is the value of y? 10
11 45. Find the area of the sector in terms of π: 46. Estimate the area of the shaded figure: 47. Find the value of x. If the answer is not an integer, represent it in the simplest radical form 48. What is the area of the figure? 49. A right triangle has the hypotenuse 18 cm and one leg 10 cm. What is the area of such triangle?? 11
12 50. Find the area of the figure below 12
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