An umbrella is made by stitching `10` triangular pieces of cloth of two different colors (see figure), each piece measuring `20 cm, 50 cm` and `50 cm.` How much cloth of each colour is required for the umbrella ?

Explanation

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)`.