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Exploring Polygons and Parallelograms: Geometry Problems and Solutions

Dive into the fascinating world of polygons and parallelograms with these geometry problems. This review covers key concepts, including the sum of interior and exterior angles of polygons, area calculations for various geometric shapes, and understanding properties of regular polygons. Solve problems involving heptagons, nonagons, rhombuses, and trapezoids, and discover practical applications like area determination and geometric probabilities. This resource is perfect for students looking to sharpen their math skills and master geometry concepts.

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Exploring Polygons and Parallelograms: Geometry Problems and Solutions

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Presentation Transcript

  1. 20 Questions Chapter 10 Review

  2. 1. Polygons The sum of the measures of the interior angles of a convex polygon is 2520. How many sides does the polygon contain? Answer

  3. Answer to Question #1 16 Sides

  4. 2. Polygons The sum of the measures of five interior angles of a heptagon is 690. The measure of the 6th angle is twice the measure of the seventh. Find the measure of the 6th angle. Answer

  5. Answer to question #2 140 degrees

  6. 3. Polygons Find the sum of the measures of the exterior angles of a convex nonagon. Answer

  7. Answer to question #3 360 degrees

  8. 4. Polygons Find the sum of the measures of the interior angles of a convex 14-gon Answer

  9. Answer to question #4 2160 degrees

  10. 5. Polygons How many sides are in a regular polygon if each interior angle measures 144º? Answer

  11. Answer to question #5 10 Sides

  12. 6. Parallelograms Find the area of a parallelogram that has vertices: A(-4, 15), B(1, 15), C(4, 10), and D(-1, 10) Answer

  13. Answer to question #6 25 square units

  14. 7. Parallelograms The length of a rectangle is 4in. More than the width. If the perimeter is 84in., find the area of the rectangle. Answer

  15. Answer to question #7 437 square inches

  16. 8. Parallelograms Find the area of a parallelogram with side lengths 8cm and 16cm and an acute angle of 45º. Answer

  17. Answer to question #8 90.51 sq. cm

  18. 9. Triangle, Rhombi, and Trapezoids Find the area of a rhombus with sides 8 inches and diagonals of 12 inches and 9 inches. Answer

  19. Answer to question #9 54 sq inches

  20. 10. Triangle, Rhombi, and Trapezoids Find the area of an isosceles trapezoid with base angles of 30º, height of and a long base of 150 cm Answer

  21. Answer to question #10 1496.49 sq cm

  22. 11. Triangle, Rhombi, and Trapezoids The area of a triangle is 160 sq cm. The height is 20 cm., Find the length of the base. Answer

  23. Answer to question #11 16 cm

  24. 12. Triangle, Rhombi, and Trapezoids Find the value of h 26cm 24cm h Answer 10cm

  25. Answer to question #12 9.23 cm

  26. 13. Regular Polygons and Circles The area of triangle ABC is 24 sq meters. If AC = 6 m and AB is a diameter, find the area of the circle C Answer A B

  27. Answer to question #13 25sq meters

  28. 14. Regular Polygons and Circles Find the area of a regular octagon with radius of 5 yd. Answer

  29. Answer to question #14 70.71 sq yds

  30. 15. Regular Polygons and circles Find the area of a regular hexagon with a side length of 22 ft. Answer

  31. Answer to question #15 1257.47 sq. ft

  32. 16. Regular Polygons Find the area of a regular decagon with an apothem of 3 cm Answer

  33. Answer to question #16 29.24 sq. cm

  34. 17. Regular Polygons Find the area of the shaded region. AB = 8 ft. C is the midpoint of AB Answer

  35. Answer to question #17 110.85 sq. ft

  36. 18. Geometric Probabilities Luke told Scott that he would arrive at the basketball game sometime between 7:20 and 7:45. Scott says that he must be on the court at 7:30. What is the probability that Luke will arrive by 7:30? Answer

  37. Answer to question #18 10/25 = 2/5 = .4

  38. 19. Geometric Probability Find the area of the sector (inside the central angle). 4 cm 120º Answer

  39. Answer to question #19 16.76 sq cm

  40. 20. Geometric Probabilities Find the probability that a point chosen at random lies in the shaded region. 10 cm Answer 10 cm

  41. Answer to question #20 .215

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