CBSE Class 10 Answered
on a circular table cover of radius 42cm , a design is formed by a girl leaving an equilateral triangle ABC in rhe middle,
Asked by akshay6098 | 09 Aug, 2020, 19:32: PM
Let a be the length of each side of the equilateral triangle ABC in the circle.
![Let space AD space be space the space altitude space of space ABC thin space from space straight A space on space BC
Altitude space of space an space equilateral space triangle equals fraction numerator square root of 3 straight a over denominator 2 end fraction
AD thin space is space also space the space median space of space triangle space ABC thin space from space straight A space on space BC space and space straight O space is space the space centroid space of space the space triangle space ABC
rightwards double arrow straight O space divides space AD space in space the space ratio space 2 colon 1
rightwards double arrow OA equals 2 over 3 AD
rightwards double arrow 42 equals 2 over 3 AD
rightwards double arrow AD equals 63 space cm
rightwards double arrow fraction numerator square root of 3 straight a over denominator 2 end fraction equals 63
rightwards double arrow straight a equals 42 square root of 3 space cm
Area space of space equilateral space triangle equals fraction numerator square root of 3 over denominator 4 end fraction straight a squared equals fraction numerator square root of 3 over denominator 4 end fraction open parentheses 42 square root of 3 close parentheses squared equals fraction numerator square root of 3 over denominator 4 end fraction cross times 42 cross times 42 cross times 3 equals 1323 square root of 3 space cm squared
Area space of space circle equals πr squared equals 22 over 7 cross times 42 cross times 42 equals 5544 space cm squared
Area space of space design space equals space 5544 space minus space 1323 square root of 3 space equals space 5544 space minus space 2288.79 space equals space 3255.21 space cm squared](https://images.topperlearning.com/topper/tinymce/cache/5fd962397a21d5c63cc2c01e057149ba.png)
Answered by Renu Varma | 11 Aug, 2020, 14:00: PM
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