**NCERT Class 9 Maths Chap 12 Heron’s Formula Solutions**

## Chapter 12: Heron’s Formula

**TEXTBOOK’S EXERCISE – 12.1**

**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?**Sol.**Each side of the triangle = a

The perimeter of the triangle = 3a

S = 3a/2

∴ Area of the signal board (triangle)

Hence, the area of the signal board = a^{2}/4 √ 3 sq. units

Now, perimeter = 180 cm

Each side of the triangle =

180/ 3 cm = 60 cm

Area of the triangle

2. **The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122 m, 22 m and 120 m (see Fig.). The advertisements yield an earning of Rs 5000 per m2 per year. A company hired one of its walls for 3 months. How much rent did it pay?**

Sol. Here, we first find the area of the triangular sidewalls.

a = 122 m, b = 120 m and c = 22 m

S = 122+120+22/2 m= 132 m

Area of the triangular sidewall

Rent of 1 m2 of the wall for 1 year = Rs 5000

∴ Rent of 1 m2 of the wall for 1 month = Rs 5000/ 12

∴Rent of the complete wall (1320 m^{2}) for 3 months

**3. 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” (see Fig.). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.**

Sol. Here a = 15 m, b = 11 m, c = 6 m

**4. Find the area of a triangle two sides of which are 18 cm and 10 cm and the perimeter is 42 cm. **

**Sol. **Here, a = 18 cm, b = 10 cm, c = ?

Perimeter of the triangle = 42 cm

⇒ a + b + c = 42 ⇒ 18 + 10 + c = 42

⇒ c = 42 – 28 = 14

**5. Sides of a triangle are in the ratio of 12 : 17 : 25 and its perimeter is 540 cm. Find its area. **

**Sol. **Let the sides of the triangle be 12x cm, 17x cm and 25x cm.

Perimeter of the triangle = 540 cm

∴ 12x + 17x + 25x = 540 ⇒ 54 x = 540

x = 540/54 =10

∴ Sides of the triangle are (12 × 10) cm, (17 × 10) cm and (25 × 10) cm i.e., 120 cm, 170 cm and 250 cm. Now, suppose a = 120 cm, b = 170 cm, c = 250 cm,

S = a+b+c/2 =540/2=270 cm

Area of the triangle