Math CentralQuandaries & Queries


Question from Pradipta, a student:

Find the area of an isoscele triangle having two equal sides of 20 cm each and angle between them 45 degree ? ( solve without trigonometric function).

There are probably many ways to find the answer. Here is the first that came to me:

Draw a square ABCD sitting on its side AB, with a diagonal AC that has length 40. Let O be the center of the square (so that AO = 20). Place the point E between A and B so that AE = 20. Your goal is to find the area of triangle AEO. Taking the base of the triangle to be AE, you just need to find the altitude from O. Observe how it is related to the square.


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