Finding the Area of a Triangle for the Area of a Segment?

I'm looking for the area if a segment. I know that the formula for the area of a triangle is 1/2bh but for some reason, my answers are turning out wrong.

Triangle 1:

Side - 11km

Angle - 60 degrees

Judging by the fact the one angle is 60 degrees, I assumed that it was equilateral.

I got the area to be 52.25 km...?

And for the other triangles:

Side - 25 yd

Side - 25 yd

Angle - 45 degrees

And

Side - 1

Side - 1

Angle - 90 degrees

1 Answer

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  • 7 years ago
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    1 i think the triangle is equilateral too, because you were only given one length. I think your answer is about right.

    The edge is 11, so half the base is 5.5, and the pythagorean theorem tells us that the height is 5.5*sqrt(3). So the area is 5.5^2*sqrt(3), which I get to be 52.3945. To check this, go to this site and enter the three sides of 11:

    http://mste.illinois.edu/dildine/tcd_files/program...

    For your next triangle, I am going to ASSUME that it's a right triangle with two 45 degree angles, each facing the 25 yd side. This is half a square, cut on the diagonal, right? So the area would be 25^2 divided by two, or 312.5 sq yd

    the last one we KNOW is a right triangle, and since the two legs of the angle are equal, we know that it also has two 45 degree angles, so the area is just 1/2.

    I am uneasy about #2. It is correct, but it seems that you weren't given all the usual information.

    Good luck.

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