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Thread: Finding an area of a triangle:

  1. #1
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    Finding an area of a triangle:

    We have a square ABCD with sides = 1, and BE=1, and AE=CE.
    What is the area of triangle ABE?

    How can I solve this?
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by thumpin_termis View Post
    We have a square ABCD with sides = 1, and BE=1, and AE=CE.
    What is the area of triangle ABE?

    How can I solve this?
    I found two ways to solve this and then stop. this is the shorter of the two methods. See the modified diagram below.

    from the description we see that $\displaystyle \triangle AEC$ is isosceles. thus if we extend the line BE, it will cut the diagonal at a right angle. from this we can the angles that you see filled in.

    now we simply use the formula $\displaystyle \mbox {Area} = \frac {1}{2}(BE)(AE) \sin 135^{ \circ} = \frac { \sqrt {2}}{4}$





    if you have any questions say so. i was kind of rushing through this and didn't explain much
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