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A floral design on the floor of a buildi...

A floral design on the floor of a building consists of 280 tiles. Each tile is in the shape of a parallelogram of altitude 3 cm and base 5 cm. Find the cost of polishing the design at the rate of 50 paise per `c m^2` .

Text Solution

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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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