Math
posted by Danielle on .
A children's play area is triangular. The sides of the play area measure 90m, 225m and 255m respectively. Calculate the area of the play area.

The semiperimeter of a triangle is half its perimeter.
The formula for the semiperimeter of a triangle with side lengths a, b, and c is:
s = ( a + b + c ) / 2
The area of a triangle can also be calculated from its semiperimeter using Heron's formula:
A = [ sqrt s * ( s  a ) * ( s  b ) * ( s  c ) ]
In this case:
a = 90
b = 225
c = 255
s = ( 90 + 225 + 255 ) / 2 = 570 / 2 = 285
A = sqrt [ s * ( s  a ) * ( s  b ) * ( s  c ) ]
A = sqrt [ 285 * ( 285  90 ) * ( 285  225 ) * ( 285  255 ) ]
A = sqrt ( 285 * 195 * 60 * 30)
A = sqrt ( 10003500 )
A = 10001.7498469 m ^ 2
approx. A = 10001.75 m ^ 2 
A = sqrt [ s * ( s  a ) * ( s  b ) * ( s  c ) ]

Thanks so much