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Answer :
Each triangular piece in an umbrella is an isosceles triangle with sides 50 cm, 50 cm, 20 cm.
Now, we know that,
\(s = \frac{a + b + c}{2}\)
\(\therefore \) \(s = \frac{50 + 50 + 20}{2} = \frac{120}{2} = 60cm\)
Now, Area of triangle
= \(\sqrt{60(60 - 50)(60 - 50)(60 - 20)}\)
(Since, Heron's formula [area = \(\sqrt{s(s - a)(s - b)(s - c)}\)])
= \(\sqrt{60 × 10 × 10 × 40}\)
= \(\sqrt{3 × 2 × 10 × 10 × 10 × 10 × 2 × 2}\)
= \(2 × 100\sqrt{6} {cm}^2\)
= \(200\sqrt{6} {cm}^2\)
Thus, from Equation (i),
Area of each triangular piece
= 2 × 432 cm = 864 cm
Since, there are 10 triangular pieces, out of which 5 & 5 are of different colours.
Hence, total area of cloth of each colour = \(5 × 200\sqrt{6} {cm}^2\) = \(1000\sqrt{6} {cm}^2\)