Perimeter-Related Questions

1. A rectangular table measures 5 m by 3 m. Find the cost of sewing its border at ₹20 per meter.

2. The sides of a triangular park are 12 m, 15 m, and 18 m. Find its perimeter.

3. A square plot has a side of 45 m. What is its perimeter?

4. A rectangular field’s length and breadth are in the ratio 7:5, and its perimeter is 240 m. Find its
dimensions.

5. A square park is surrounded by a path 2 m wide. If the side of the park is 50 m, find the outer perimeter.

6. A farmer walks around a triangular field of sides 50 m, 60 m, and 70 m. What distance does he cover in
4 rounds?

7. A hexagonal park has sides measuring 10 m each. Find the perimeter of the park.

8. A garden is in the shape of a pentagon with sides 8 m each. Find its perimeter.

9. If the perimeter of a square and rectangle are both 64 m, which has a greater area?

10. A circular garden has a circumference of 88 m. What is its radius?

Area of Rectangles and Squares

11. Find the area of a rectangle with dimensions 12 m and 8 m.

12. A square has a side of 18 cm. Find its area.

13. A rectangular plot is 25 m long and 15 m wide. Find the cost of growing grass on it at ₹10 per square
meter.

14. A room measures 10 m × 6 m. If tiles of side 2 m are used, how many tiles are required?

15. A photo frame has an area of 240 cm² and a length of 20 cm. Find its breadth.

16. A square garden has a perimeter of 96 m. Find its area.

17. A rectangular floor of dimensions 10 m × 8 m needs carpeting. If the carpet costs ₹200 per square
meter, what is the total cost?

18. A square-shaped lawn has a side of 12 m. Find the cost of replanting grass on it at ₹25 per square
meter.

19. A rectangular field of dimensions 60 m by 45 m has a path of width 3 m all around it. Find the area of the
path.

20. A square’s area is 256 cm². Find its perimeter.

21. • Find the cost of stitching a border around a rectangular tablecloth of length 6 m and width 3 m at ₹30 per
metre.
22. • A rectangular field has a length and breadth in the ratio 4:5. If its perimeter is 360 m, find its length and
breadth.
23. • A square park has a side of 24 m. Find the distance covered by Riya if she jogs around the park 5 times.
24. • The length and breadth of a rectangular room are 12 m and 9 m, respectively. Find its perimeter.
25. • The perimeter of a square and a rectangle are equal. The square has a side of 16 m, and the rectangle has a
breadth of 10 m. Find the area of both shapes.
26. • A rectangular park is 100 m long and 50 m wide. A path of 5 m wide is built along its boundary. Find the
area of the path.
27. • Find the cost of reaping a rectangular field of dimensions 120 m × 80 m at ₹25 per square metre. 1
 28. • A square garden has a side of 30 m. Find the cost of fencing it at ₹45 per metre.
29. • A family photograph of dimensions 30 cm × 20 cm needs a frame. Find the perimeter and the cost of
framing at ₹12 per cm.
30. • A square is divided into four equal smaller squares. If the area of the original square is 64 m², find the side
length of each smaller square.
31. • The length of a rectangular hall is twice its breadth, and its perimeter is 96 m. Find its area.
32. • The cost of carpeting a square room at ₹150 per square metre is ₹8100. Find the side of the room.
33. • A square-shaped farm has a perimeter of 400 m. Find the cost of fencing it at ₹50 per metre.
34. • The length of a rectangle is increased by 20%, and its breadth is reduced by 10%. Find the percentage
change in its area.
35. • The diagonal of a square is 14√2 cm. Find its area and perimeter.
36. • The area of a rectangle is 300 cm², and its length is 15 cm. Find its breadth and perimeter.
37. • A square is enlarged such that its side is increased by 30%. By what percentage does its area increase?
38. • The sides of two squares are in the ratio 3:4. Find the ratio of their areas.
39. • The length of a rectangle is thrice its breadth, and its area is 192 cm². Find its length and breadth.
40. • A rectangular field is twice as long as it is wide. If it were 4 m longer and 4 m narrower, it would be a
square. Find its dimensions.

Triangle Area and Dimensions

1. A triangle has a base of 10 cm and a height of 14 cm. Find its area.

2. A right-angled triangle has a base of 24 m and a hypotenuse of 26 m. Find its area.
3. A triangular park has a perimeter of 48 m, and two of its sides are 20 m and 12 m. Find the third side.
4. The area of a triangle is 120 cm², and its height is 15 cm. Find its base.
5. A triangular plot has a base of 18 m and height 10 m. Find the cost of planting grass on it at ₹12 per square
meter.
6. 6. A triangular plot has sides 7 m, 9 m, and 12 m. Find its perimeter.

7. The height of a triangle is 8 cm, and its area is 48 cm². Find its base.

8. A triangular field has a base of 20 m and height 15 m. Find the cost of cultivating it at ₹50 per square
metre.

9. The perimeter of a triangle is 40 cm. Two sides measure 12 cm and 15 cm. Find the third side.

10. A right-angled triangle has a base of 6 cm and a hypotenuse of 10 cm. Find its height and area.

11. The ratio of base to height in a triangle is 3:2. If its area is 180 cm², find its base and height.

12. The base of a triangle is doubled, and its height is halved. How does its area change?

13. A triangle with base 10 cm and height 12 cm is divided into two smaller triangles by a line parallel to its
base. Find the area of each smaller triangle.

14. The base and height of a triangle are in the ratio 5:3. If the area is 75 cm², find the base and height.

15. A triangular garden has sides 13 m, 14 m, and 15 m. Find its perimeter.

16. A triangle has sides 8 cm, 15 cm, and 17 cm. Find its area using Heron’s formula.
17. The sides of a triangle are 13 m, 14 m, and 15 m. Find its area and the height corresponding to the largest side.
18. A right-angled triangle has a hypotenuse of 25 cm and one side of 24 cm. Find its area and the other side.
19. The base of a triangle is increased by 25%, and its height is decreased by 20%. Find the percentage change in
its area.
20. A triangle with sides 9 cm, 12 cm, and 15 cm is divided into two smaller triangles by an altitude. Find the area
of each smaller triangle.
21. The perimeter of an equilateral triangle is 36 cm. Find its area.
22. The lengths of two sides of a triangle are 5 cm and 12 cm. Find the possible range for the third side.
23. The altitude of a triangle is reduced to half, and the base is doubled. How does the area change?
24. The sides of a triangle are in the ratio 3:4:5. If its perimeter is 36 cm, find its area. 2
 25. A triangle has a base of 10 cm and a height of 8 cm. A line parallel to the base divides it into two parts of
equal area. Find the height of the smaller triangle.

Circles

1. A circle has a radius of 7 cm. Find its circumference and area.

2. The area of a circle is 154 cm². Find its radius.

3. The diameter of a circular track is 21 m. Find its perimeter.

4. A wire of length 88 cm is bent into a circle. Find its radius and area.

5. A circular garden has a circumference of 176 m. Find its area.

6. A semicircular park has a diameter of 20 m. Find its perimeter.

7. A circular path of radius 10 m is surrounded by a path 2 m wide. Find the area of the path.

8. Two circles have radii 10 cm and 15 cm. Find the difference in their areas.

9. A wire is bent into a square of side 11 cm. If the same wire is bent into a circle, find its radius.

10. The circumference of a circle is 66 cm. Find its radius.

11. • Find the area and circumference of a circle with a radius of 14 cm.
12. • The diameter of a circle is 21 cm. Find its circumference.
13. • A circular pond has a diameter of 28 m. Find the cost of fencing it at ₹25 per metre.
14. • A wire of length 132 cm is bent into a circle. Find its radius and area.
15. • The circumference of a circle is 88 cm. Find its radius and area.
16. • The radius of a circular field is tripled. How does its area and circumference change?
17. • A semicircular garden has a diameter of 20 m. Find its perimeter and area.
18. • A circle and a square have the same perimeter. The square has a side length of 14 cm. Find the radius of the
circle.
19. • The circumference of a circular park is 176 m. A path 2 m wide is built inside it. Find the area of the path.
20. • A circular track has a radius of 35 m. How much distance does a runner cover in 4 complete rounds?
21. • Find the radius of a circle whose area is 154 cm².
22. • A circular plot has a radius of 35 m. Find the cost of leveling it at ₹15 per square metre.
23. • A wheel has a diameter of 84 cm. How far will it travel in 50 rotations?
24. • A circle is inscribed in a square of side 28 cm. Find the area of the circle and the shaded region outside it.
25. • The circumference of a circle is equal to the perimeter of a square of side 44 cm. Find the radius of the
circle.
26. • A wire of length 220 cm is bent into the shape of a semicircle. Find the radius and area of the semicircle.
27. • The radius of a circle is halved. By what percentage does its area decrease?
28. • The diameter of a circular plate is 30 cm. Find the cost of polishing it at ₹10 per square cm.
29. • A sector of a circle has a radius of 21 cm and a central angle of 60°. Find its area.
30. • A circular garden of radius 28 m is surrounded by a path 3 m wide. Find the cost of paving the path at ₹25
per square metre.

Composite Figures and Irregular Shapes

1. A circular flower bed of radius 4 m is surrounded by a square pavement of side 10 m. Find the area of
the pavement.

2. A rectangular plot of 50 m × 40 m has two circular flower beds of radius 5 m each. Find the area left
after planting the flower beds.

3. A square park has a circular fountain of radius 7 m at its center. The side of the park is 30 m. Find the
remaining area.
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4. A triangular garden has a base of 18 m and height 12 m. Surrounding it is a rectangular path 2 m wide.
Find the area of the path.

5. A circular track of radius 15 m is surrounded by a rectangular field of dimensions 50 m by 40 m. Find the

remaining area.

6. • A rectangular plot has dimensions 40 m × 30 m. Two circular flower beds of radius 4 m each are cut out.
Find the remaining area.
7. • A square is divided into a rectangle and two equal triangles. If the side of the square is 12 cm, find the area
of each shape.
8. • A garden has a rectangular section of 20 m × 10 m and a semicircular section with a diameter of 10 m. Find
the total area of the garden.
9. • A circular park of radius 21 m has a rectangular walkway of dimensions 12 m × 6 m built inside it. Find the
remaining area of the park.
10. • A square has a side of 16 m. A circle is inscribed within it. Find the area of the shaded region outside the
circle.
11. • Two circular paths of radii 7 m and 9 m are built concentrically. Find the area of the ring-shaped path.
12. • A rectangular field has a semicircular area of radius 14 m attached to one of its shorter sides. Find the total
area of the field if the rectangle measures 40 m × 20 m.
13. • A playground is shaped like a parallelogram with a triangular garden at one end. The parallelogram has a
base of 25 m and height 15 m, and the triangle has a base of 12 m and height 10 m. Find the total area.
14. • A rectangular paper of size 30 cm × 20 cm has a circular hole of radius 5 cm cut out. Find the remaining
area of the paper.
15. • A hexagon is divided into six equilateral triangles. If the side length of the hexagon is 10 cm, find the area
of one triangle.
16. • A rectangle of dimensions 12 cm × 8 cm has a semicircle on one of its shorter sides. Find the total
perimeter of the shape.
17. • A square has a circle inscribed in it, and the circle has another square inscribed in it. Find the area of the
shaded region if the side of the outer square is 20 cm.
18. • A rectangular playground of size 40 m × 30 m has a triangular flower bed of base 10 m and height 8 m in
one corner. Find the remaining area of the playground.
19. • A circular field has a rectangular section of dimensions 20 m × 12 m carved out of it. If the radius of the
field is 15 m, find the remaining area.
20. • A square garden has a circular pond of radius 7 m in its center. The side of the garden is 20 m. Find the area
of the garden excluding the pond.
21. • A circle of radius 14 cm has a square inscribed in it. Find the area of the square.
22. • Two concentric circles have radii of 14 cm and 10 cm. Find the area of the ring-shaped region between
them.
23. • A rectangular park has dimensions 60 m × 40 m. A path of width 5 m is built inside, parallel to its sides.
Find the area of the path.
24. • A square is inscribed in a circle of radius 14 cm. Find the area of the square.
25. • A semicircular garden has a diameter of 28 m. A rectangular pathway of dimensions 10 m × 5 m is built
inside it. Find the remaining area.

11. A circular jogging track has an outer radius of 20 m and an inner radius of 15 m. Find the area of the
track.

12. A rectangular lawn of dimensions 80 m × 50 m is surrounded by a flower bed 4 m wide on all sides. Find
the area of the flower bed.

13. A square playground has a side of 60 m. A rectangular parking area of size 20 m × 10 m is built in one
corner. Calculate the remaining area.

14. A circular park has a radius of 28 m. A circular walking path of 2 m width surrounds it. Find the area of
the walking path.

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15. A rectangular plot of size 50 m × 30 m has a smaller rectangular vegetable patch of size 20 m × 10 m in
one corner. Find the remaining area.

16. A triangular park has sides of 40 m, 30 m, and 20 m. A 2 m wide walking path runs along its boundary
inside. Find the area of the path.

17. A semicircular stage has a diameter of 10 m. A 1 m wide path runs along its outer edge. Find the area of
the path.

18. A circular playground has a radius of 25 m. A 3 m wide path surrounds it outside. Calculate the area of
the path.

19. A rectangular garden of size 100 m × 50 m has a pathway of width 2 m running all around it inside. Find
the area of the pathway.

20. A square park of side 40 m has a 5 m wide path along its border outside. Find the area of the path.

Advanced Real-Life Scenarios

21. A circular park has an inner walking path with a radius of 20 m and an outer walking path with a radius
of 25 m. Find the area between the two paths.

22. A square-shaped building of side 30 m has a rectangular swimming pool of dimensions 15 m × 10 m at

its center. Find the remaining floor area.

23. A rectangular field of size 120 m × 80 m has a path 5 m wide running inside along its boundary.
Calculate the area of the path and the remaining field.

24. A circular ground has a radius of 10 m. A 2 m wide circular flower bed is created inside it, along the
boundary. Find the area of the flower bed.

25. A rectangular courtyard of dimensions 40 m × 30 m has a circular garden of radius 10 m in the middle.
Calculate the area of the remaining space.

26. A triangular park with sides 50 m, 40 m, and 30 m has a 2 m wide jogging path inside, along its edges.
Calculate the area of the jogging path.

27. A square-shaped parking lot of side 100 m has a square garden of side 30 m in its center. Find the
remaining area of the parking lot.

28. A rectangular plot of dimensions 80 m × 60 m has a square swimming pool of side 20 m in one corner.
Find the area of the remaining plot.

29. A circular sports ground has a radius of 25 m. A 3 m wide circular seating area surrounds it outside. Find
the area of the seating area.

30. A square floor has a circular rug with a radius of 6 m placed in its center. The side of the floor is 20 m.
Find the area of the floor excluding the rug.

31. • A rectangular farm has a length of 150 m and breadth of 80 m. A 10 m wide road runs through the middle
of the farm, dividing it into two equal parts. Find the total area of the road.
32. • A circular swimming pool has a diameter of 50 m. Around it, a walkway of 4 m is constructed. Find the
area of the walkway.
33. • A piece of cloth of size 1 m × 2 m is cut into small square pieces of side 10 cm. How many pieces can be
cut?
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34. • A square tile of side 15 cm is used to cover a rectangular floor of dimensions 3 m × 2 m. Find the number
of tiles required.
35. • The cost of painting a circular wall of radius 10 m is ₹500. Find the cost of painting a similar wall with
radius 20 m.
36. • The perimeter of a rectangle is 48 cm. If its length is 16 cm, find its breadth and area.
37. • A semicircular window has a diameter of 2 m. Find the cost of glass required to cover it at ₹200 per square
metre.
38. • A square of side 8 cm is divided into four equal rectangles. Find the area of each rectangle.
39. • A square plot of side 50 m is surrounded by a 2 m wide path. Find the cost of paving the path at ₹60 per
square metre.
40. • A triangular garden has sides 13 m, 14 m, and 15 m. Find the cost of fencing it at ₹50 per metre.
41. • A circular park has an inner walking path with a radius of 20 m and an outer walking path with a radius of
25 m. Find the area between the two paths.
42. • A square-shaped building of side 30 m has a rectangular swimming pool of dimensions 15 m × 10 m at its
center. Find the remaining floor area.
43. • A rectangular field of size 120 m × 80 m has a path 5 m wide running inside along its boundary. Calculate
the area of the path and the remaining field.
44. • A circular ground has a radius of 10 m. A 2 m wide circular flower bed is created inside it, along the
boundary. Find the area of the flower bed.
45. • A rectangular courtyard of dimensions 40 m × 30 m has a circular garden of radius 10 m in the middle.
Calculate the area of the remaining space.
46. • A triangular park with sides 50 m, 40 m, and 30 m has a 2 m wide jogging path inside, along its edges.
Calculate the area of the jogging path.
47. • A square-shaped parking lot of side 100 m has a square garden of side 30 m in its center. Find the
remaining area of the parking lot.
48. • A rectangular plot of dimensions 80 m × 60 m has a square swimming pool of side 20 m in one corner. Find
the area of the remaining plot.
49. • A circular sports ground has a radius of 25 m. A 3 m wide circular seating area surrounds it outside. Find
the area of the seating area.
50. • A square floor has a circular rug with a radius of 6 m placed in its center. The side of the floor is 20 m. Find
the area of the floor excluding the rug

Miscellaneous Questions

1. A square’s side is increased by 20%. Find the percentage increase in its area.

2. A rectangle’s length is halved, and its breadth is tripled. What is the percentage change in its area?

3. The area of a square is doubled. By what percentage does its side increase?

4. A rectangular field of dimensions 60 m by 40 m has a triangular flower bed of base 20 m and height 15
m at one corner. Find the area of the remaining field.

5. A circular park of radius 30 m has a rectangular pathway of dimensions 50 m × 10 m inside it. Find the
remaining area of the park

6. • A rectangular floor measuring 12 m × 8 m is to be covered with square tiles of side 40 cm. Find the number
of tiles required.
7. • The perimeter of a square is 64 cm. Find its area.
8. • A farmer builds a fence around his square plot of side 50 m. If the cost of fencing is ₹80 per metre, find the
total cost.
9. • The area of a rectangle is 72 m², and its length is 12 m. Find its breadth and perimeter.
10. • A wire is in the shape of a rectangle with length 10 cm and breadth 6 cm. If it is bent into a square, find the
side of the square.
11. • A playground is shaped like a parallelogram with a base of 30 m and a height of 20 m. Find its area.
12. • A square park has a side of 60 m. Two paths, each 3 m wide, are built parallel to its sides. Find the
remaining area of the park.
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 13. • A circular flower bed of radius 5 m is surrounded by a path 2 m wide. Find the area of the path.
14. • A triangular park has a base of 50 m and height 30 m. Find the cost of fencing it at ₹12 per metre.
15. • A square lawn is divided into four equal parts. If the side of the square is 40 m, find the area of each part.

Scenario-Based Questions

1. A square park has a side length of 50 m. A 3 m wide pathway runs along its border inside the park. Find
the area of the pathway.

2. A circular garden has a radius of 15 m. A 2 m wide path surrounds it outside. Find the area of the path.

3. A rectangular field of dimensions 60 m × 40 m has a 5 m wide path running all around it inside the
boundary. Find the area of the path.

4. A circular swimming pool of diameter 20 m has a surrounding path of 2 m width. Calculate the area of
the path.

5. A square courtyard has a circular fountain with a radius of 5 m at its center. The side of the courtyard is
20 m. Find the area of the remaining space.

6. A rectangular park of size 100 m × 80 m has a rectangular pond of size 40 m × 30 m in one corner.
Calculate the remaining area of the park.

7. A rectangular playground has dimensions 60 m × 40 m. A 3 m wide track runs inside it along the entire
boundary. Find the area of the track.

8. A semicircular garden has a diameter of 30 m. A path of width 3 m surrounds it. Calculate the area of
the path.

9. A circular plot of radius 50 m has a rectangular area of 20 m × 10 m in the middle. Calculate the area of
the remaining portion of the plot.

10. A square park of side 25 m has a circular pond with a radius of 7 m in the center. Find the area of the
park excluding the pond.