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NCERT Class 9 Maths Chap 12 Heron’s Formula Solutions

## Chapter 12: Heron’s Formula

#### TEXTBOOK’S EXERCISE – 12.1

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 = a2/4 √ 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 m2) 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