# A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm, and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm^{2}.

**Solution:**

Given: Dimensions of the triangular tiles.

By using Heron’s formula, we can calculate the area of triangle.

Heron's formula for the area of a triangle, Area = √s(s - a)(s - b)(s - c)

Where a, b and c are the sides of the triangle, and s = Semi-perimeter = Half the Perimeter of the triangle = (a + b + c)/2

We have the dimensions of sides of each triangular tile.

a = 35 cm, b = 28 cm, c = 9 cm

Semi Perimeter(s) = (a + b + c)/2

s = (35 + 28 + 9)/2

s = 72/2

s = 36 cm

By using Heron’s formula,

Area of each triangular tile = √s(s - a)(s - b)(s - c)

= √36(36 - 35)(36 - 28)(36 - 9)

= √36 × 1 × 8 × 27

= 36√6 cm^{2}

Area of a 1 triangular tile = 36√6 cm^{2}

Area of 16 triangular tile = 16 × 36√6 cm^{2}

= 16 × 36 × 2.45 cm^{2}

= 1411.2 cm^{2}

Since, the cost of polishing 1cm^{2} of tiles is 50p or ₹ 0.5

Therefore, the cost of polishing 1411.2 cm^{2} area of tiles = 1411.2 cm^{2} × 0.5 = ₹ 705.60

**Video Solution:**

## A floral design on a floor is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm, and 35 cm (see Fig. 12.18). Find the cost of polishing the tiles at the rate of 50p per cm².

### Class 9 Maths NCERT Solutions - Chapter 12 Exercise 12.2 Question 8:

**Summary:**

It is given that there is a floral design on a floor that is made up of 16 tiles which are triangular, the sides of the triangle being 9 cm, 28 cm, and 35 cm. We have found that the cost of polishing all the tiles at the rate of 50p per cm^{2} is ₹ 705.60.