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

Solution

For one triangular piece
a = 20 cm b = 50 cm c = 50 cm
$therefore space space space space space space straight s equals fraction numerator straight a plus straight b plus straight c over denominator 2 end fraction space space space space space space space space space space equals space fraction numerator 20 plus 50 plus 50 over denominator 2 end fraction equals 120 over 2 equals 60 space cm$
Area of one triangle
$equals square root of straight s left parenthesis straight s minus straight a right parenthesis left parenthesis straight s minus straight b right parenthesis left parenthesis straight s minus straight c right parenthesis end root equals space square root of 60 left parenthesis 60 minus 20 right parenthesis left parenthesis 60 minus 50 right parenthesis left parenthesis 60 minus 50 right parenthesis end root equals space square root of 60 left parenthesis 40 right parenthesis left parenthesis 10 right parenthesis left parenthesis 10 right parenthesis end root equals 200 square root of 6 space cm squared$
∴ Area of five triangles of one colour
$equals 5 left parenthesis 200 square root of 6 right parenthesis space cm squared equals 1000 square root of 6 space cm squared$
Hence, 1000 $square root of 6$ cm² of each colour is required for the umbrella.

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Statistics

An umbrella is made by stitching 10 triangular pieces of cloth of two different colours (see figure), 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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