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An umbrella is made by stitching 10 tria...

An umbrella is made by stitching 10 triangular pieces of cloth of two different colour, 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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In an umbrella, triangular piece is an isosceles triangle with sides 50 cm, 50 cm, 20 cm.
Now, `s=(50+50+20)/(2)` cm
`rArr s= 60 `cm
`:.` Area of each triangular piece`=sqrt(60(60-50)(60-50)(60-20)) " "`(by Heron's formula)
`=sqrt(60xx10xx10xx40)`
`=sqrt(6xx10xx10xx10xx4xx10)`
`=200 sqrt(6) cm^(2)`
Since, there are 10 triangular piece, in those of them 5-5 are of different colours. Hence, total area of cloth of each colour `=5xx200sqrt(6) cm^(2) = 1000 sqrt(6) cm^(2)`.
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