Class 9 NCERT Solutions Maths Chapter 10 - Heron's Formula
Ex. 10.1
Heron's Formula Exercise Ex. 10.1
Solution 1
Side of traffic signal board = a
Perimeter of traffic signal board = 3
a
Perimeter of traffic signal board = 3
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_b9ccb383b0c73c26cfb3ff194a86e235.png)
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_a07156ccb0344a18de12f2463ad4c0df.png)
By Heron's formula
Perimeter of traffic signal board = 180 cm
Side of traffic signal board![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_22ab9748f6405f79d8e4018d3ad30ef5.png)
Side of traffic signal board
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_22ab9748f6405f79d8e4018d3ad30ef5.png)
Using equation (1), area of traffic of signal board ![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_ca88426b5d97ae534f05620f0efe9488.png)
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_ca88426b5d97ae534f05620f0efe9488.png)
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/887_b252166c600f7705f1cbb769d1af137d.png)
Solution 2
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
![](https://images.topperlearning.com/topper/bookquestions/888_p17.JPG)
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![Double click to edit](https://images.topperlearning.com/topper/bookquestions/888_c2b94c1eefde7aba83ac4f4a8b838c42.png)
Rent of 1 m2 area per month = Rs
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/888_c2b94c1eefde7aba83ac4f4a8b838c42.png)
Rent of 1320 m2 area for 3 months ![Double click to edit](https://images.topperlearning.com/topper/bookquestions/888_8fd1bacb0de78e6a6ca705a9bbdd57fd.png)
= Rs.(5000
330) = Rs.1650000
So, company had to pay Rs.1650000.
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/888_8fd1bacb0de78e6a6ca705a9bbdd57fd.png)
= Rs.(5000
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/888_b9ccb383b0c73c26cfb3ff194a86e235.png)
So, company had to pay Rs.1650000.
Solution 3
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
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
.
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/889_da252a2ce654d48118d4cc35d88f755b.png)
Solution 4
Let third side of triangle be x.
Perimeter of given triangle = 42 cm
18 cm + 10 cm + x = 42
x = 14 cm
Perimeter of given triangle = 42 cm
18 cm + 10 cm + x = 42
x = 14 cm
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/890_7d29fedaff9a8f376a5367e765b7172d.png)
By Heron's formula
Solution 5
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.
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.
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/891_ea361a01b6ee275bdacf1e7f2dec1bf5.png)
By Heron's formula
So, area of this triangle will be 9000 cm2.
Solution 6
Let third side of this triangle be x.
Perimeter of triangle = 30 cm
12 cm + 12 cm + x = 30 cm
x = 6 cm
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/892_623fd0c3d47c92190d82b9c9ea0d50fd.png)
Perimeter of triangle = 30 cm
12 cm + 12 cm + x = 30 cm
x = 6 cm
![Double click to edit](https://images.topperlearning.com/topper/bookquestions/892_623fd0c3d47c92190d82b9c9ea0d50fd.png)
By Heron's formula