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 `50 p\ p e r\ c m^2`.

Explanation

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 = sqrt(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 = `sqrt(s(s - a)(s - b)(s - c))`

= `sqrt(36(36 - 35)(36 - 28)(36 - 9))`

= `sqrt(36 × 1 × 8 × 27)`

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