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. 12.9). The advertisements yield an earning of ₹5000 per m^{2}per year. A company hired one of its walls for 3 months. How much rent did it pay?

**Solution**

The sides of the triangle are 122 m, 22 m and 120 m.

Perimeter of the triangle is 122 + 22 + 120 = 264m

Semi perimeter of triangle (s) = 264/2 = 132 m

Using heron's formula,

Area of the advertisement = √s (s-a) (s-b) (s-c)

= √132(132 - 122) (132 - 22) (132 - 120) m^{2}

= √132 × 10 × 110 × 12 m^{2}

= 1320 m^{2}

Rent of advertising per year = ₹ 5000 per m^{2}

Rent of one wall for 3 months = ₹ (1320 × 5000 × 3)/12 = ₹ 1650000

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. 12.10 ). If the sides of the wall are 15 m, 11 m and 6 m, find the area painted in colour.

**Solution**

Sides of the triangular wall are 15 m, 11 m and 6 m.

Semi perimeter of triangular wall (s) = (15 + 11 + 6)/2 m = 16 m

Using heron's formula,

Area of the message = √s (s-a) (s-b) (s-c)

= √16(16 - 15) (16 - 11) (16 - 6) m^{2}

= √16 × 1 × 5 × 10 m^{2 }= √800 m^{2}

= 20√2 m^{2}

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

**Solution**

Two sides of the triangle = 18cm and 10cm

Perimeter of the triangle = 42cm

Third side of triangle = 42 - (18+10) cm = 14cm

Semi perimeter of triangle = 42/2 = 21cm

Using heron's formula,

Area of the triangle = √s (s-a) (s-b) (s-c)

= √21(21 - 18) (21 - 10) (21 - 14) cm^{2}

= √21 × 3 × 11 × 7 m^{2}

= 21√11 cm^{2}

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

**Solution**

Ratio of the sides of the triangle = 12 : 17 : 25

Let the common ratio be x then sides are 12x, 17x and 25x

Perimeter of the triangle = 540cm

12x + 17x + 25x = 540 cm

⇒ 54x = 540cm

⇒ x = 10

Sides of triangle are,

12x = 12 × 10 = 120cm

17x = 17 × 10 = 170cm

25x = 25 × 10 = 250cm

Semi perimeter of triangle(s) = 540/2 = 270cm

Using heron's formula,

Area of the triangle = √s (s-a) (s-b) (s-c)

= √270(270 - 120) (270 - 170) (270 - 250)cm^{2}

= √270 × 150 × 100 × 20 cm^{2}

= 9000 cm^{2}