NCERT Class 9 Maths Solutions Chapter - 12 Heron's Formula, Ex - 12.1

Ex - 12.1

Question 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?

Solution

Side of traffic signal board = a
Perimeter of traffic signal board = 3

By Heron's formula

Perimeter of traffic signal board = 180 cm
Side of traffic signal board

Using equation (1), area of traffic of signal board

Question 2. The triangular side walls of a flyover have been used for advertisements. The sides of the walls are 122m, 22m, and 120m (see the given figure). 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?

Solution

We may observe that sides of triangle a, b, c are of 122 m, 22 m, and 120 m respectively
   Perimeter of triangle = (122 + 22 + 120) m
                 2s = 264 m
                   s = 132 m
   By Heron's formula

Rent of 1 m² area per year = Rs.5000
Rent of 1 m² area per month = Rs

Rent of 1320 m² area for 3 months

= Rs.(5000

330) = Rs.1650000
So, company had to pay Rs.1650000.

Question 3. There is a slide in the park. One of its side walls has been painted in the same colour with a message "KEEP THE PARK GREEN AND CLEAN" (see the given figure). If the sides of the wall are 15m, 11m, and 6m, find the area painted in colour.

Solution

We may observe that the area to be painted in colour is a triangle, having its sides as 11 m, 6 m, and 15 m.
   Perimeter of such triangle = (11 + 6 + 15) m
                2 s = 32 m
                       s = 16 m
By Heron's formula

So, the area painted in colour is

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

Solution

Let third side of triangle be x.
Perimeter of given triangle = 42 cm
18 cm + 10 cm + x = 42
x = 14 cm

By Heron's formula

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

Solution

Let the common ratio between the sides of given triangle be x.
So, side of triangle will be 12x, 17x, and 25x.
Perimeter of this triangle = 540 cm
             12x + 17x + 25x = 540 cm
                         54x = 540 cm
                            x = 10 cm
Sides of triangle will be 120 cm, 170 cm, and 250 cm.