Question 319797: What is the area of a triangle with lengths of sides of 20, 31 and 43?
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! Use Heron's Formula to find your area. The triangle has 3 different sides and so this tells me that it is a scalene triangle.
Let sqrt = square root
Let A = area of scalene triangle
Let a + b + c = sides of triangle
Let s = half of the triangle's perimeter
s = (a + b + c)/2
The formula is A = sqrt{s(s - a)(s - b)(s - c)}
The given sides:
a = 20
b = 31
c = 43
We need to find the value of letter s as step one. Just plug and chug.
s = (20 + 31 + 43)/2
s = 94/2
s = 47
We can now use the formula given above.
A = sqrt{s(s - a)(s - b)(s - c)}
We also plug and chug.
A = sqrt{47(47 - 20)(47 - 31)(47 - 43)}
A = sqrt{47(27)(16)(4)}
A = sqrt{47(1728)}
A = sqrt{81216}
A = 284.9842101, Which can be rounded to the nearest unit (or ones place) to make the answer 285.
To learn more about Heron's Formula, copy and paste the link below.
http://www.mathsisfun.com/geometry/herons-formula.html
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