Geometry

Practice Exercise

Very Easy (Difficulty Level-1):

1. Frank, the fencemaker, needs to fence in a rectangular yard. He fenced in the entire yard except fro one 40-foot side of the yard. The yard has an area of 280 square feet. How many feet of fence does Frank use?

2. 40% of Anderson leaving room is covered by a rectangular carpet that is 4 feet by 9 feet. What is the area of her living room floor?

3. If the perimeter of rectangular floor bed is 30 feet, and its area is 44 square feet, what is the length of each of its shorter side?

4. There’s a rectangular parking lot with a length of 2x and a width of x. What is the ratio of the perimeter of the parking lot, in terms of x?

5. A cube has edge of 5 inches long. What is the ratio of cubes surface area to its volume?

Easy (Difficulty Level-2):

6. A rectangular solid has a square base, with each side of the base measuring 4 meters. If the volume of the rectangular solid is 112 cubic meters, what is the surface area of the rectangular solid?

7. If the length of an edge of cube A is one third the length of an edge of cube B, what is the ratio of volume of cube A to volume of cube B?

8. A circular lawn with a radius of 5 meters is surrounded by a circular walkway that is 4 meters wide. What is the area of the walkway?

9. Beginning in Town A, Biker Bob rides his bike 10 miles west, 3 miles north, 5-miles east, and then 9 miles north to Town B. How far apart are Town A and Town B?

10. Bilal can run π meters every 2 seconds. If the circular track has a radius of 75 meters, how long does it take him to run twice around the track?

Easy (Difficulty Level-3):

11. In previous question, if Bilal moves on the jumbo track, which has radius of 200 meters (as compared to the previous track with radius of 75 meters). Ordinarily Bilal runs 8 laps on normal track. How many laps in jumbo track will he has to run in order to have the same work-out?

12. A swimming pool has a length of 30 meters, a width of 10 meters and an average depth of 2 meters. If a hose can fill the pool at rate of 0.5 cubic meter per minutes, how many hours will it take the hose to fill the pool?

13. A cylinder has a surface area of 360π, and is 3 units tall. What is the diameter of the cylinder circular base?

14. Triangle ABC is inscribed in a circle, such that AC is the diameter of the circle. If AB has length of 8, and BC has length of 15, what is the circumference of the circle?

15. Red Giant cola comes in two sizes, Giant and Super-Giant. Each comes in cylindrical container. Giant size sells for $1.20. The Super-Giant size has twice the height and its circular base has twice the radius of Giant size. If price per ml Red Giant cola is the same, how much does the Super-Giant container cost?

Hard (Difficulty Level-4):

16. Jane has to paint a cylindrical column that is 14 feet high and that has a circular base with a radius of 3 feet. If one bucket of paint will cover 10π square feet, how many buckets does Jane need to buy in order to paint the column, including the top and bottom?

17. A circular flowerbed takes up half the area of a square lawn. If an edge of the lawn is 200 feet long, what is the radius of the flowerbed? (Answer this in terms of π).

18. ABCD is a quadrilateral, with AB parallel to CD as shown in figure above. E is a point between C and D, such that AE represents the height of quadrilateral ABCD. If AB is 4 inches long, AE is 5 inches long and area of triangle AED is 12.5 square inches, what is the area of ABCD?

19. ABCD is parallelogram as shown in the figure above. The ratio of DE to EC is 1 : 3. If quadrilateral ABCE has area of 21, what is the are of ABCD?

20. ABCD is a square picture frame as shown in figure above. EFGH is a square inscribed within ABCD as a space for a picture. The area of EFGH is equals to the area of the picture frame, which is area of ABCD minus area of EFGH. If length of AB is 6 inches, what is length of EF in inches?

Very Hard & Tricky (Difficulty Level-5):

21. What is measure of angle x in the figure above?

22. In triangle ABC above, if AD = DB = DC, what is the measure of angle x?

23. The points of six pointed star consists of six identical equilateral triangles, with each side of 4cm as shown above. What is the area of the entire star?

24. A rectangular box has dimensions 12 inches by 10 inches by 8 inches. What is the largest possible volume of a right cylinder that is placed inside the box?

25. How many small rectangular boxes of dimensions 2 × 3 × 5 can be placed inside a large box of dimensions 20 × 22 × 25, such that only minimum possible empty space remain in large box after placing smaller boxes?

Answer Sheet:

1. 54 feet
2. 90
3. 4

4. ³⁄_x

5. ⁶⁄₅

6. 144
7. 1 to 27
8. 56π
9. 13
10. 10 minutes
11. 3 laps
12. 20
13. 24
14. 17π
15. $9.6
16. 11

17. ^√20000⁄_√π

18. 35
19. 24
20. 3√2
21. 50°
22. 10°
23. 48√3
24. 200π
25. 352