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Heron’s Formula
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26/07/2021 10:42 am
Topic starter
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.). Find the cost of polishing the tiles at the rate of 50p per cm2.
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26/07/2021 10:47 am
The semi perimeter of the each triangular shape
= \(\frac{28+9+35}{2}\) cm = 36 cm
By using Heron’s formula,
The area of each triangular shape will be
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{36(36 - 35)(36 - 28)(36 - 9)}\)
= \(\sqrt{36 \times 1 \times 8 \times 27}\)cm2
= 36√6 cm2
= 88.2 cm2
Now, the total area of 16 tiles = 16 × 88.2 cm2
= 1411.2 cm2
It is given that the polishing cost of tiles = 50 paise/cm2
∴ The total polishing cost of the tiles = Rs. (1411.2 × 0.5)
= Rs. 705.6