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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 the given figure). Find the cost of polishing the tiles at the rate of 50p per cm^2. - Mathematics

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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 the given figure). Find the cost of polishing the tiles at the rate of 50p per cm2.

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Solution

It can be observed that

Semi-perimeter of each triangular-shaped tile,

`s=(35+28+9)/2=36cm`

By Heron’s formula,

`"Area of triangle "=sqrt(s(s-a)(s-b)(s-c))`

`"Area of each tile "=[sqrt(36(36-35)(36-28)(36-9))]cm^2`

                           `=[sqrt(36xx1xx8xx27)]cm^2`

                           `=36sqrt6 cm^2`

                            = (36 x 2.45) cm^2

                            = 88.2 cm2

Area of 16 tiles = (16 × 88.2) cm2= 1411.2 cm2

Cost of polishing per cm2 area = 50 p

Cost of polishing 1411.2 cm2 area = Rs (1411.2 × 0.50) = Rs 705.60

Therefore, it will cost Rs 705.60 while polishing all the tiles.

Concept: Application of Heron’s Formula in Finding Areas of Quadrilaterals
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APPEARS IN

NCERT Class 9 Maths
Chapter 12 Heron's Formula
Exercise 12.2 | Q 8 | Page 207

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