Math CentralQuandaries & Queries


Question from Udit, a student:

A long time ago Mr Gibson found an island shaped as a triangle with three straight shores of length 3 km,4 km and 5 km. He declared an 'exclusion zone' around his island and forbade anyone to come within 1 km of his shore. What was the area of his exclusion zone?

Please explain it to the fullest!,
Your assistance is appreciated!

Hi Udit,

The exclusion zone consists of a 1 mile wide rectangular strip along each side and a sector of a circle at each vertex of the triangle. Here is a close up at one vertex with the exclusion zone coloured blue.


You can calculate the area of the circular section of the exclusion zone if you know the measure of its central angle. What do you know about the measures of a triangle that has side lengths 3, 4 and 5 units?


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