SOLUTION: find the area of the triangle with the following dimension, a=4cm,b=13,c=15cm

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Question 1143340: find the area of the triangle with the following dimension, a=4cm,b=13,c=15cm
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
Picking c=15 for the base, and angle A using Law Of Cosines,

area is %281%2F2%29%2A15%2A13sin%2814.25%29.

Answer by greenestamps(13209) About Me  (Show Source):
You can put this solution on YOUR website!


Heron's formula gives the area of a triangle in terms of the lengths of the three sides:

A+=+sqrt%28s%28s-a%29%28s-b%29%28s-c%29%29

where s is the semiperimeter.

The formula looks scary; but it is easy to use.

(1) find the semiperimeter: s+=+%28a%2Bb%2Bc%29%2F2+=+%284%2B13%2B15%29%2F2+=+16
(2) find the differences between the semiperimeter and each side: s-a+=+16-4+=+12; s-b+=+16-13+=+3; s-c+=+16-15+=+1
(3) evaluate: A+=+sqrt%2816%2A12%2A3%2A1%29+=+sqrt%2816%2A36%2A1%29+=+4%2A6+=+24

The area of the triangle is 24 square units.