## EXERCISE 12.1

#### Page No 202:

#### 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?

#### Answer:

Side of traffic signal board = *a*

Perimeter of traffic signal board = 3 × *a*

By Heron’s formula,

Perimeter of traffic signal board = 180 cm

Side of traffic signal board

Using equation (1), area of traffic 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 m^{2} per year. A company hired one of its walls for 3 months. How much rent did it pay?

#### Answer:

The sides of the triangle (i.e., *a*, *b*, *c*) are of 122 m, 22 m, and 120 m respectively.

Perimeter of triangle = (122 + 22 + 120) m

2*s* = 264 m

*s* = 132 m

By Heron’s formula,

Rent of 1 m^{2} area per year = Rs 5000

Rent of 1 m^{2} area per month = Rs

Rent of 1320 m^{2} area for 3 months =

= Rs (5000 × 330) = Rs 1650000

Therefore, the company had to pay Rs 1650000.

#### Page No 203:

#### 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.

#### Answer:

It can be observed 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 a triangle = (11 + 6 + 15) m

2 *s* = 32 m

*s* = 16 m

By Heron’s formula,

Therefore, 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.

#### Answer:

Let the third side of the triangle be *x*.

Perimeter of the 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.

#### Answer:

Let the common ratio between the sides of the given triangle be *x*.

Therefore, the side of the triangle will be 12*x*, 17*x*, and 25*x*.

Perimeter of this triangle = 540 cm

12*x* + 17*x* + 25*x* = 540 cm

54*x* = 540 cm

*x* = 10 cm

Sides of the triangle will be 120 cm, 170 cm, and 250 cm.

By Heron’s formula,

Therefore, the area of this triangle is 9000 cm^{2}.

#### Question 6:

An isosceles triangle has perimeter 30 cm and each of the equal sides is 12 cm. Find the area of the triangle.

#### Answer:

Let the third side of this triangle be *x*.

Perimeter of triangle = 30 cm

12 cm + 12 cm + *x* = 30 cm

*x* = 6 cm

By Heron’s formula,