# NCERT Solutions for Class 9 Maths Chapter 12

Download NCERT Solutions for Class 9 Maths Chapter 12 Exercise 12.1 and Exercise 12.2 of Heron’s Formula in English Medium and Hindi Medium free to use online. NCERT Solutions for Class 9 all subjects and other chapters of maths are also given in PDF format. NCERT Books in ZIP format and  NCERT Books in PDF format are available to download.

## NCERT Solutions for Class 9 Maths Chapter 12

If you need solutions in Hindi, Click for Hindi Medium solutions of 9 Maths Chapter 12         Previous Chapter: Chapter 11

NCERT Solutions 9 Maths: Main Page

Next Chapter: Chapter 13

### 9 Maths Chapter 12 Exercise 12.1 & Exercise 12.2 in Hindi        Previous Chapter: Chapter 11

NCERT Solutions 9 Maths: Main Page

Next Chapter: Chapter 13

To get the solutions in English, Click for English Medium solutions.

##### Class 9 Maths – Heron’s Formula
###### Important Extra Questions with Answers
1. Find the area of a triangle whose base and altitudes are 8 cm and 5 cm. [Answer: 20 cm²]
2. Find the area of an equilateral triangle whose sides are 4 cm each. [Answer: 4√3 cm²]
3. If sum of two sides of a triangle is 17 cm and its perimeter is 30 cm, then what is the length of third side? [Answer: 13 cm]
4. If perimeter of a triangle is 24 cm and sides are in the ratio 2:1:3, then find the longest side? [Answer: 12 cm]
5. If each sides of a triangle is doubled then how many times the area of triangle increased? [Answer: 3 times]
6. If area of a triangle is 50 cm² and one of its sides is 10 cm then find the length of corresponding altitude. [Answer: 10 cm]
7. The area of an equilateral triangle is 16√3 cm² then what will be the length of each side of that triangle? [Answer: 8 cm]
8. A square has each side of 5 cm. Find the length of one of its diagonals. [Answer: 5√2 cm]
9. If a parallelogram has length is 10 cm and 8 cm then find the area of a triangle made by its diagonal. [Answer: 40 cm²]
10. If area of a triangle is doubled to its area then what is the percentage increased in the area of triangle? [Answer: 100%]
11. If one side of a triangle is 9.5 m and its corresponding altitude is 12 m then what will be the area of triangle. [Answer: 57 m²]
12. The ratio between the sides of a triangle are 3:5:7 and its perimeter is 300 cm find the sides of triangle. [Answer: 60 cm, 100 cm, 140 cm]
13. Find the cost of fencing the ground in the form of a triangle with sides 16 m, 12 m and 18 m. The rate of fencing is ₹ 25 per meter. [Answer: ₹ 1150]
14. Find the area of isosceles triangle whose non equal sides of 12 cm having the corresponding altitude is 7.5 cm. [Answer: 45 cm²]
15. In a right angled triangle the sides make the right angle are 10 cm and 24 cm. Find the area of triangle. [Answer: 120 cm²]
16. If in a triangle AB = 15 cm, BC = 14 cm and AC = 13 cm. Find the area of ∆ABC and hence its altitude on BC. [Answer: 84 cm², 12 cm]
17. The diagonals of a rhombus are 10 cm and 24 cm. Find its area and perimeter. [Answer: 120 cm², 52 cm]
18. Find the area of a triangle or region whose sides are 1.6 m, 1.2 m and 2.0 m. [Answer: 0.96 m²]
19. The perimeter of a triangle shaped ground is 420 m and its sides are in the ratio 6:7:8. Find the area of ground. [Answer: 2100√15 m²]
20. Find the area of rhombus whose perimeter is 100 m and one of whose diagonal is 30 m. [Answer: 300 m²]
21. The sides of a triangle 5 cm, 12 cm and 13 cm. Find the cost of painting on the triangle at the rate of ₹ 30 per cm². [Answer: ₹ 900]
22. If perimeter of a triangle is x cm and its sides are p, q and r cm. What will be the area of triangle? Use the Heron’s formula.
23. A Triangular Park ABC has sides 120 m, 80m and 50 m. A gardener Dhani Ram has to put a fence all around it and also plant some trees inside the garden to get clean air.

(i) Find the cost of fencing it at the rate of ₹ 50 per meter. Leaving space 5 cm wide for the gate on one side.

(ii) Find its area where Dhani Ram may plant the tree.

(iii) What values of Dhani Ram do you assess here? [Answer: (i) ₹ 12250, (ii) 375√15 m², (iii) Caring about environment clean air]

1. A triangular hoarding of dimension 11m, 6 m and 15 m is used for commercial activities. The hoarding yield an earning of ₹ 5000 per m² per month. Calculate the total earning by the hoarding in a month. [Use √2 = 1.7] [Answer: ₹ 510000]