Moderate Level Questions
1. Find the breadth of a rectangular plot of land, if its area is 440 m2 and the length is 22 m. Also find its perimeter.
2. The perimeter of a rectangular sheet is 100 cm. If the length is 35 cm, find its breadth. Also find the area.
3. Bharti runs 10 times around a square field of side 80 m. Her sister Sushmita runs 8 times around a rectangular field with length 150 m and breadth 60m. Who covers more distance? By how much?
4. The area of a rectangular sheet is 550 cm2. If the length of the sheet is 25 cm, what is its width? Also find the perimeter of the rectangular sheet.
5. A door-frame of dimensions 3 m × 2 m is fixed on the wall of dimension 12 m × 10 m. Find the total labour charges for painting the wall if the labour charges for painting 1 m2 of the wall is ₹3.50.
6. Avika wants to fence the garden in front of her house, on three sides with lengths 20 m, 12 m and 12 m. Find the cost of fencing at the rate of ₹250 per metre.
7. A wire is in the shape of a square of side 10 cm. If the wire is rebent into a rectangle of length 12 cm, find its breadth. Which encloses more area, the square or the rectangle?
8. The length and the breadth of a rectangular piece of land are 550 m and 320 m respectively. Find (i) its area (ii) the cost of the land, if 1 m2 of the land costs ₹11,000.
9. The area of a square and a rectangle are equal. If the side of the square is 40 cm and the breadth of the rectangle is 25 cm, find the length of the rectangle. Also, find the perimeter of the rectangle.
10. A room is 4.5 m long and 4 m wide. The floor of the room is to be covered with tiles of size 15 cm by 10 cm. Find the cost of covering the floor with tiles at the rate of ₹4.50 per tile.
11. The area of a square park is the same as of a rectangular park. If the side of the square park is 60 m and the length of the rectangular park is 90 m, find the breadth of the rectangular park.
12. A wire is in the shape of a rectangle. Its length is 40 cm and breadth is 22 cm. If the same wire is rebent in the shape of a square, what will be the measure of each side? Also find which shape encloses more area?
13. The perimeter of a rectangle is 40 m. Its length is four metres less than five times its breadth. Find the area of the rectangle.
14. The perimeter of a rectangle is 130 cm. If the breadth of the rectangle is 30 cm, find its length. Also find the area of the rectangle.
15. A door of length 2 m and breadth 1 m is fitted in a wall. The length of the wall is 4.5 m and the breadth is 3.6 m. Find the cost of white washing the wall, if the rate of white washing the wall is ₹20 per m2.
16. A wall of a room is of dimensions 5 m × 4 m. It has a window of dimensions 1.5 m × 1 m and a door of dimensions 2.25 m × 1 m. Find the area of the wall which is to be painted.
17. A hedge boundary needs to be planted around a rectangular lawn of size 72 m × 18 m. If 3 shrubs can be planted in a metre of hedge, how many shrubs will be planted in all?
18. A wall of a room is of dimensions 5 m × 4 m. It has a window of dimensions 1.5 m × 1 m and a door of dimensions 2.25 m × 1 m. Find the area of the wall which is to be painted.
19. The perimeter of a rectangle is 40 m. Its length is four metres less than five times its breadth. Find the area of the rectangle.
20. Ramesh grew wheat in a rectangular field that measured 32 metres long and 26 metres wide. This year he increased the area for wheat by increasing the length but not the width. He increased the area of the wheat field by 650 square metres. What is the length of the expanded wheat field?
21. In a parallelogram ABCD, AB = 7.2 cm and the perpendicular from C on AB is 4.5 cm. One of the sides and the corresponding height of a parallelogram are 4 cm and 3 cm respectively. Find the area of the parallelogram.
22. The two sides of the parallelogram ABCD are 6 cm and 4 cm. The height corresponding to the base CD is 3 cm. Find the
- (i) area of the parallelogram;
- (ii) height corresponding to the base AD.
23. PQRS is a parallelogram. QM is the height from Q to SR and QN is the height from Q to PS. If SR = 12 cm and QM = 7.6 cm. Find
- (a) the area of the parallelogram PQRS;
- (b) QN, if PS = 8 cm.
24. DL and BM are the heights on sides AB and AD respectively of parallelogram ABCD. If the area of the parallelogram is 1470 cm2, AB = 35 cm and AD = 49 cm, find the length of BM and DL.
25. Area of an isosceles triangle is 48 cm2. If the altitudes corresponding to the base of the triangle is 8 cm, find the perimeter of the triangle.
26. A rectangular field is 48 m long and 12 m wide. How many right triangular flower beds can be laid in this field, if sides including the right angle measure 2 m and 4 m, respectively?
27. ABCD is a parallelogram in which AE is perpendicular to CD. Also AC = 5 cm, DE = 4 cm, and the area of ∆AED = 6 cm2. Find the perimeter and area of ABCD.
28. Perimeter of a parallelogram shaped land is 96 m and its area is 270 square metres. If one of the sides of this parallelogram is 18 m, find the length of the other side. Also, find the lengths of altitudes l and m.
29. ∆ABC is right angled at A. AD is perpendicular to BC. If AB = 5 cm, BC = 13 cm and AC = 12 cm, Find the area of ∆ABC. Also find the length of AD.
30. ∆ABC is isosceles with AB = AC = 7.5 cm and BC = 9 cm. The height AD from A to BC is 6 cm. Find the area of ∆ABC. What will be the height from C to AB i.e., CE?
31. ABCD is a parallelogram, in which AB = 8 cm, AD = 6 cm and altitude AE = 4 cm. Find the altitude corresponding to side AD.
32. 4 squares each of side 10 cm have been cut from each corner of a rectangular sheet of paper of size 100 cm × 80 cm. From the remaining piece of paper, an isosceles right triangle is removed whose equal sides are each of 10 cm length. Find the area of the remaining part of the paper.
33. Circumference of a circle is 33 cm. Find its area.
34. If the circumference of a circular sheet is 154 m, find its radius. Also find the area of the sheet (take π = 22/7).
35. A gardener wants to fence a circular garden of diameter 21 m. Find the length of the rope he needs to purchase, if he makes 2 rounds of fence. Also find the cost of the rope, if it costs ₹4 per meter (take π = 22/7).
36. From a circular sheet of radius 4 cm, a circle of radius 3 cm is removed. Find the area of the remaining sheet (take π = 3.14).
37. Saima wants to put a lace on the edge of a circular table cover of diameter 1.5 m. Find the length of the lace required and also find its cost if one meter of the lace costs ₹15 (take π = 3.14).
38. Find the cost of polishing a circular table-top of diameter 1.6 m, if the rate of polishing is ₹15 per square metre (take π = 3.14).
39. Shazli took a wire of length 44 cm and bent it into the shape of a circle. Find the radius of that circle. Also find its area. If the same wire is bent into the shape of a square, what will be the length of each of its sides? Which figure encloses more area, the circle or the square (take π = 22/7)?
40. Find the total cost of wooden fencing around a circular garden of diameter 28 m, if 1m of fencing costs ₹300.
41. A circle of radius 2 cm is cut out from a square piece of an aluminium sheet of side 6 cm. What is the area of the left over aluminium sheet (take π = 3.14)?
42. The circumference of a circle is 31.4 cm. Find the radius and the area of the circle (take π = 3.14).
43. Find the area of a square inscribed in a circle whose radius is 7 cm.
44. A circular flower bed is surrounded by a path 4 m wide. The diameter of the flower bed is 66 m. What is the area of this path (π = 3.14)?
45. Priyanka took a wire and bent it to form a circle of radius 14 cm. Then she bent it into a rectangle with one side 24 cm long. What is the length of the wire? Which figure encloses more area, the circle or the rectangle?
46. The moon is about 384000 km from earth and its path around the earth is nearly circular. Find the length of path described by moon in one complete revolution (take π = 3.14).
47. How much distance, in metres, a wheel of 25 cm radius will cover if it rotates 350 times?
48. A circular pond is surrounded by a 2 m wide circular path. If outer circumference of circular path is 44 m, find the inner circumference of the circular path. Also find area of the path.
49. A circular flower garden has an area of 314 m2. A sprinkler at the centre of the garden can cover an area that has a radius of 12 m. Will the sprinkler water the entire garden (take π = 3.14)?
50. How many times a wheel of radius 28 cm must rotate to go 352 m (take π = 22/7)?
51. The minute hand of a circular clock is 15 cm long. How far does the tip of the minute hand move in 1 hour (take π = 3.14)?
52. A rectangular park is 45 m long and 30 m wide. A path 2.5 m wide is constructed outside the park. Find the area of the path.
53. A path 5 m wide runs along inside a square park of side 100 m. Find the area of the path. Also find the cost of cementing it at the rate of ₹250 per 10 m2.
54. Two cross roads, each of width 5 m, run at right angles through the centre of a rectangular park of length 70 m and breadth 45 m and parallel to its sides. Find the area of the roads. Also find the cost of constructing the roads at the rate of ₹105 per m2.
55. A garden is 90 m long and 75 m broad. A path 5 m wide is to be built outside and around it. Find the area of the path. Also find the area of the garden in hectare.
56. A 3 m wide path runs outside and around a rectangular park of length 125 m and breadth 65 m. Find the area of the path.
57. A picture is painted on a cardboard 8 cm long and 5 cm wide such that there is a margin of 1.5 cm along each of its sides. Find the total area of the margin.
58. A rectangular shaped swimming pool with dimensions 30 m × 20 m has 5 m wide cemented path along its length and 8 m wide path along its width. Find the cost of cementing the path at the rate of ₹200 per m2.
59. A veranda of width 2.25 m is constructed all along outside a room which is 5.5 m long and 4 m wide. Find
- (i) the area of the veranda
- (ii) the cost of cementing the floor of the veranda at the rate of ₹200 per m2.
60. A table cover of dimensions 3 m 25 cm × 2 m 30 cm is spread on a table. If 30 cm of the table cover is hanging all around the table, find the area of the table cover which is hanging outside the top of the table. Also find the cost of polishing the table top at ₹16 per square metre.
61. The dimensions of a plot are 200 m × 150 m. A builder builds 3 roads which are 3 m wide along the length on either side and one in the middle. On either side of the middle road he builds houses to sell. How much area did he get for building the houses?
62. A path 1 m wide is built along the border and inside a square garden of side 30 m. Find
- (i) the area of the path;
- (ii) the cost of planting grass in the remaining portion of the garden at the rate of ₹40 per m2.
63. Two cross roads, each of width 10 m, cut at right angles through the centre of a rectangular park of length 700 m and breadth 300 m and parallel to its sides. Find the area of the roads. Also find the area of the park excluding cross roads. Give the answer in hectares.
64. Through a rectangular field of length 90 m and breadth 60 m, two roads are constructed which are parallel to the sides and cut each other at right angles through the centre of the fields. If the width of each road is 3 m, find
- (i) the area covered by the roads;
- (ii) the cost of constructing the roads at the rate of ₹110 per m2.