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
To calculate the area of a triangular play area, we can use Heron's formula. Heron's formula states that the area (A) of a triangle with sides a, b, and c can be calculated as:
A = sqrt(s * (s - a) * (s - b) * (s - c))
where s is the semi-perimeter of the triangle, calculated as:
s = (a + b + c) / 2
Let's calculate the area of the given triangular play area:
a = 90m
b = 225m
c = 255m
First, calculate the semi-perimeter:
s = (90 + 225 + 255) / 2 = 570 / 2 = 285
Next, calculate the area using Heron's formula:
A = sqrt(285 * (285 - 90) * (285 - 225) * (285 - 255))
= sqrt(285 * 195 * 60 * 30)
= sqrt(613575000)
Now, let's calculate the square root using a calculator or approximation method:
sqrt(613575000) ≈ 24769.912
Therefore, the area of the play area is approximately 24,769.912 square meters.