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Heron’s Formula
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26/07/2021 10:28 am
Topic starter
An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see Fig.), each piece measuring 20 cm, 50 cm and 50 cm. How much cloth of each colour is required for the umbrella?
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26/07/2021 10:31 am
For each triangular piece, The semi perimeter will be
s = \(\frac{50+50+20}{2}\)cm
= \(\frac{120}{2}\) cm
= 60 cm
Using Heron’s formula,
Area of the triangular piece
= \(\sqrt{s(s - a)(s - b)(s - c)}\)
= \(\sqrt{60(60 - 50)(60 - 50)(60 - 20)}\)cm2
= \(\sqrt{60 \times 10 \times 10 \times 40}\)cm2
= 200√6 cm2
∴ The area of all the triangular pieces
= 5 × 200√6 cm2
= 1000√6 cm2