Question

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.

Answer 1

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

Answer 2

A = sqrt [ s * ( s - a ) * ( s - b ) * ( s - c ) ]

Answer 3

Thanks so much