CBSE Class 9 Herons Formula Sure Shot Questions

Advanced Study Material for Class 9 Mathematics: Chapter 12 Herons Formula

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Practice Class 9 Mathematics Resources: Chapter 12 Herons Formula

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CBSE Class 9 Herons Formula Sure Shot Questions. There are many more useful educational material which the students can download in pdf format and use them for studies. Study material like concept maps, important and sure shot question banks, quick to learn flash cards, flow charts, mind maps, teacher notes, important formulas, past examinations question bank, important concepts taught by teachers. Students can download these useful educational material free and use them to get better marks in examinations.  Also refer to other worksheets for the same chapter and other subjects too. Use them for better understanding of the subjects.

1. Find the area of a triangle whose sides are 35 cm, 45 cm and 50 cm.

2. An isosceles triangle has perimeter 30 cm and each of its equal sides is 12 cm. Find its area. (use √15= 3.88)

3. The measure of one side of a right triangular field is 4.2 m. If the difference of the lengths of hypotenuse and the other is 14m, find the sides of the triangle and its area.

4. Find the area of the quadrilateral ABCD given in the below figure

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5. The perimeter of a rhombus is 40cm. If one of its diagonal is 16cm, find the area of the rhombus.

6. Two parallel sides of a trapezium are 60cm and 77cm and the other sides are 25cm and 26cm. Find the area of the trapezium.

7. Find the area of quadrilateral ABCD in which AD = 24cm, √BAD = 900 and B, C and D form an equilateral triangle of side 26cm. (use √3 =1.73)

8. The height of an equilateral triangle measures 9cm. Find its area, correct to two places of decimals (use √3=1.73)

9. A triangular park ABC has sides 120m, 80m and. A gardener Dhania has to put a fence all around it and also plant grass inside. How much area does she need to plant? Find the cost of fencing it with barbed wire at the rate of Rs 20 per metre leaving a space 3m wide for a gate on one side.

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10. A traffic signal board, indicating ‘SCHOOL AHEAD’, is an equilateral triangle with side ‘a’. Find the area of the signal board, using Heron’s formula. If its perimeter is 180 cm, what will be the area of the signal board?

11. A park, in the shape of a quadrilateral ABCD, has ∠C = 90º, AB = 9 m, BC = 12 m, CD = 5 m and AD = 8 m. How much area does it occupy?

12. Find the area of a quadrilateral ABCD in which AB = 3 cm, BC = 4 cm, CD = 4 cm, DA = 5 cm and AC = 5 cm.
 
13. There is a slide in a park. One of its side walls has been painted in some colour with a message “KEEP THE PARK GREEN AND CLEAN”. If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.
 CBSE Class 9 Herons Formula Sure Shot Questions
 
14. Students of a school staged a rally for cleanliness campaign. They walked through the lanes in two groups. One group walked through the lanes AB, BC and CA; while the other through AC, CD and DA. Then they cleaned the area enclosed within their lanes. If AB = 9 m, BC = 40 m, CD = 15 m, DA = 28 m and ∠B = 90º, which group cleaned more area and by how much? Find the total area cleaned by the students (neglecting the width of the lanes).
 CBSE Class 9 Herons Formula Sure Shot Questions
 
15. Sanya has a piece of land which is in the shape of a rhombus. She wants her one daughter and one son to work on the land and produce different crops. She divided the land in two equal parts.
If the perimeter of the land is 400 m and one of the diagonals is 160 m, how much area each of them will get for their crops?
 
16. Find the area of a triangle, two sides of which are 8 cm and 11 cm and the perimeter is 32 cm.
 
17. A triangle has sides 35 cm, 54 cm and 61 cm long. Find its area. Also find smallest of its altitudes.
 
18. The sides of a triangular plot are in the ratio 3 : 5 : 7 and its perimeter is 300 m. Find its area.
 
19. A triangle and a parallelogram have the same base and the same area. If the sides of the triangle are 26 cm, 28 cm and 30 cm, and the parallelogram stands on the base 28 cm, find the height of the parallelogram.
 
20. A rhombus shaped field has green grass for 18 cows to graze. If each side of the rhombus is 30 m and its longer diagonal is 48 m, how much area of grass field will each cow be getting?
 
21. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540cm. Find its area.
 
22. The base of an isosceles triangle is 10 cm and one of its equal sides is 13 cm. Find its area.
 
23. Find the area of a right triangle in which the sides containing the right angle measure 20 cm and 15 cm.
 
24. An umbrella is made by stitching 10 triangular pieces of cloth of two different colours each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
 CBSE Class 9 Herons Formula Sure Shot Questions
 
25. A kite in the shape of a square with a diagonal 32 cm and an isosceles triangle of base 8 cm and sides 6 cm each is to be made of three different shades as shown in Fig.. How much paper of each shade has been used in it?
CBSE Class 9 Herons Formula Sure Shot Questions 
 
26. A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm and 35 cm. Find the cost of polishing the tiles at the rate of 50p per cm2.
 
27. Kamla has a triangular field with sides 240 m, 200 m, 360 m, where she grew wheat. In another triangular field with sides 240 m, 320 m, 400 m adjacent to the previous field, she wanted to grow potatoes and onions. She divided the field in two parts by joining the mid-point of the longest side to the opposite vertex and grew patatoes in one part and onions in the other part.
How much area (in hectares) has been used for wheat, potatoes and onions? (1 hectare = 10000 m2).
CBSE Class 9 Herons Formula Sure Shot Questions 
 
28. A field is in the shape of a trapezium whose parallel sides are 25 m and 10 m. The non-parallel sides are 14 m and 13 m. Find the area of the field.
 
29. An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.
 
30. Find the area of a triangle two sides of which are 18cm and 10cm and the perimeter is 42cm.
 
31. The sides of a triangular field are 41 m, 40 m and 9 m. Find the number of rose beds that can be prepared in the field, if each rose bed, on an average needs 900 cm2 space.
 
32. Calculate the area of the shaded region in
CBSE Class 9 Herons Formula Sure Shot Questions 
 
33. Find the cost of laying grass in a triangular field of sides 50 m, 65 m and 65 m at the rate of Rs 7 per m2.
 
34. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 13 m, 14 m and 15 m. The advertisements yield an earning of Rs 2000 per m2 a year. A company hired one of its walls for 6 months. How much rent did it pay?
 
35. From a point in the interior of an equilateral triangle, perpendiculars are drawn on the three sides. The lengths of the perpendiculars are 14 cm, 10 cm and 6 cm. Find the area of the triangle.
 
36. The perimeter of an isosceles triangle is 32 cm. The ratio of the equal side to its base is 3 : 2. Find the area of the triangle.
 
37. A field in the form of a parallelogram has sides 60 m and 40 m and one of its diagonals is 80 m long. Find the area of the parallelogram.
 
38. The perimeter of a triangular field is 420 m and its sides are in the ratio 6 : 7 : 8. Find the area of the triangular field.
 
39. The sides of a quadrilateral ABCD are 6 cm, 8 cm, 12 cm and 14 cm (taken in order) respectively, and the angle between the first two sides is a right angle. Find its area.
 
40. A rhombus shaped sheet with perimeter 40 cm and one diagonal 12 cm, is painted on both sides at the rate of Rs 5 per m2. Find the cost of painting.
 
41. Find the area of a parallelogram given in the below Figure. Also find the length of the altitude from vertex A on the side DC.
 CBSE Class 9 Herons Formula Sure Shot Questions
 
42. Find the area of the trapezium PQRS with height PQ given in the below Figure
CBSE Class 9 Herons Formula Sure Shot Questions
 
43. If each side of a triangle is doubled, then find the ratio of area of the new triangle thus formed and the given triangle.
 
44. The perimeter of a triangle is 50 cm. One side of a triangle is 4 cm longer than the smaller side and the third side is 6 cm less than twice the smaller side. Find the area of the triangle.
 
45. The area of a trapezium is 475 cm2 and the height is 19 cm. Find the lengths of its two parallel sides if one side is 4 cm greater than the other.
 
46. A rectangular plot is given for constructing a house, having a measurement of 40 m long and 15 m in the front. According to the laws, a minimum of 3 m, wide space should be left in the front and back each and 2 m wide space on each of other sides. Find the largest area where house can be constructed.
 
47. A field is in the shape of a trapezium having parallel sides 90 m and 30 m. These sides meet the third side at right angles. The length of the fourth side is 100 m. If it costs Rs 4 to plough 1m2 of the field, find the total cost of ploughing the field.
 
48. The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. Find the length of its longest altitude.
 
49. In the below Fig, △ABC has sides AB = 7.5 cm, AC = 6.5 cm and BC = 7 cm. On base BC a parallelogram DBCE of same area as that of △ABC is constructed. Find the height DF of the parallelogram.
CBSE Class 9 Herons Formula Sure Shot Questions 
 
50. A design is made on a rectangular tile of dimensions 50 cm × 70 cm as shown in below Figure. The design shows 8 triangles, each of sides 26 cm, 17 cm and 25 cm. Find the total area of the design and the remaining area of the tile.
CBSE Class 9 Herons Formula Sure Shot Questions

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Mathematics Class 9 Exam Resources: Chapter 12 Herons Formula

Comprehensive Study Resources for Chapter 12 Herons Formula

Access comprehensive study material for Chapter 12 Herons Formula, including revision notes, concept maps, and high-probability questions. These resources are designed in alignment with the latest 2026 CBSE syllabus for Class 9 Mathematics to support effective exam preparation.

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Maximize your grade potential by utilizing Class 9 Mathematics practice papers in tandem with these structured notes. All printable assignments and interactive mock tests on our platform are updated for the 2026 session and available free of charge.

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Our advanced study package for Chapter 12 Herons Formula includes detailed concepts, diagrams, Mind Maps, and explanation of complex topics to ensure Class 9 students learn as per syllabus for 2026 exams.

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Yes, our subject matter experts have updated the Chapter 12 Herons Formula material to align with the rationalized NCERT textbooks and have removed deleted topics and added new competency-based questions.