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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 = \(5 × 200\sqrt{6} {cm}^2\) = \(1000\sqrt{6} {cm}^2\)

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- NCERT solutions for class 9 maths chapter 1 Number Systems
- NCERT solutions for class 9 maths chapter 2 Polynomials
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