Welcome to the Heron’s Formula Mock Test for Class 9 Mathematics, thoughtfully designed according to the latest CBSE and NCERT guidelines.
This test serves as an excellent opportunity for students to revise, practice, and master the important concepts from the chapter “Heron’s Formula” in a fun and interactive way.

Whether you’re preparing for your school exams, unit tests, or simply aiming to strengthen your understanding of Geometry, this mock test will help you evaluate your knowledge and build confidence.

1. A student is given three sticks of lengths 12 cm, 6 cm and 4 cm respectively. He is asked to make a triangle and find the area of the triangle formed, area of the triangle is

 
 
 
 

2. If the side of rhombus is 10 cm and one diagonal is 12 cm, then area of rhombus is

 
 
 
 

3. Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:

Assertion (A): The area of an isosceles triangle having base = 24 cm and each of the equal sides equal to 13 cm is 60 cm2.
Reason (R): If 2s = (a + b + c), where a, b, c are the sides of a triangle, then area =

 
 
 
 

4. A triangular colourful scenery is made in a wall with sides 50 cm, 50 cm and 80 cm. A golden thread is to hang from the vertex so as to just reach the side 80 cm. How much length of golden thread is required ?

 
 
 
 

5. Given three sticks of lengths 10 cm, 5 cm and 3 cm. A triangle is formed using the sticks, then area of the triangle will be

 
 
 
 

6. The length of each side of an equilateral triangle having an area of 9cm2 is

 
 
 
 

7. The area of an equilateral triangle with side 4 cm is

 
 
 
 

8. A rhombus shaped field has green grass for 36 cows to graze. If each side of the field is 30 m and longer diagonal is 48 m, then how much area of grass each cow will get, if 216 m2 of area is not to be grazed.

 
 
 
 

9. A gardener has to put double fence all round a triangular path with sides 120 m, 80 m and 60 m. In the middle of each sides, there is a gate of width 10 m. Find the length of the wire needed for the fence.

 
 
 
 

10. The sides of a triangle are 56 cm, 60 cm and 52 cm long. Then the area of the triangle is

 
 
 
 

11. The base of a right triangle is 8 cm and hypotenuse is 10 cm. Its area will be

 
 
 
 

12. Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:

Assertion (A): The area of a triangle having two sides 8 cm and 11 cm and perimeter 32 cm is 8  cm2.
Reason (R): Area of the triangle is 

 
 
 
 

13. Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:

Assertion (A): The sides of a triangle are in the ratio 10:20:30 then its perimeter is 600. Then the area of the triangle is 450 square cm.
Reason (R): Perimeter of the triangle is s = a + b + c, where a, b and c are sides of a triangle.

 
 
 
 

14. In a family with two sons, a father has a field in the form of a right angled triangle with sides 18 m and 40 m. He wants to give independent charge to his sons, so he divided the field in the ratio 2 : 1 : 1, the bigger part he kept for himself and divided remaining equally among the sons, find the total area distributed to the sons.

 
 
 
 

15. The area of an isosceles triangle having base 2 cm and the length of one of the equal sides 4 cm, is

 
 
 
 

16. Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:

Assertion (A): Area of an equilateral triangle having each side equal to 4 cm is 4  sq cm.
Reason (R): Area of an equilateral triangle having
each side a is a2  sq units.

 
 
 
 

17. The sides of a triangle are 35 cm, 54 cm and 61 cm, respectively. The length of its longest altitude

 
 
 
 

18. The cost of levelling the ground in the form of triangle having sides 51 m, 37 m, 20 m at the rate of 3 per m2 is

 
 
 
 

19. Area of an equilateral triangle, of each side 2a units is

 
 
 
 

20. The edges of a triangular board are 6 cm, 8 cm and 10 cm. The cost of painting it at 0.09 per cm2 is

 
 
 
 

21. Two sides of a triangle are 8 cm and 11 cm and perimeter of triangle is 32 cm. Then value of ‘s’ is

 
 
 
 

22. Direction: In the following Questions, the Assertion and Reason have been put forward. Read the statements carefully and choose the correct alternative from the following:

Assertion (A): The area of an equilateral triangle having side 4 cm is 3 cm2.
Reason (R): The area of an equilateral triangle having each side a is sq units.

 
 
 
 

23. The area of an equilateral triangle is  cm2, then half of the perimeter of the triangle is

 
 
 
 

24. The area of an isosceles triangle having base 4 cm and length of one of equal sides as 6 cm is

 

 
 
 
 

25. A traffic signal board is equilateral in shape, with words ‘SCHOOL AHEAD’ with on it. The perimeter of the board is 180 cm, then the area of the signal board is

 
 
 
 

26. If the base of a right-angled triangle is 15 cm and its hypotenuse is 25 cm, then find its area.

 
 
 
 

27. An isosceles right triangle has area 8 cm2. The length of its hypotenuse is

 
 
 
 

28. The perimeter of an equilateral triangle is 60 m. The area is

 
 
 
 

29. An umbrella is made by stitching 8 triangular pieces of cloth of two different colours. Each piece measuring 20 cm, 50 cm, 50 cm. How much cloth of each colour is required?

 
 
 
 

30. A kite in the shape of a square of diagonal 20 cm and an equilateral triangle of base 5 cm is made of three different shades, as shown. How much paper for the shaded portion has been used?

 
 
 
 

Question 1 of 30