Question

A children's play area is triangular. The sides of the play area measure 100 m 250 m and 275 m respectively. Find the area

Answer 1

Heron's Formula for the area of a triangle :

A = sqrootÿ[ s ( s - a ) ( s - b ) ( s - c ) ]

s is half the perimeter .

s = ( a + b + c ) / 2

a = ( 100 + 250 + 275 ) / 2 = 625 / 2 = 312.25 m


A = sqrootÿ[ s ( s - a ) ( s - b ) ( s - c ) ]

A = sqrootÿ[ 312.25 ( 312.25 - 100 ) ( 312.25 - 250 ) ( 312.25 - 275 ) ]

A = sqroot ( 312.25 * 212.25 * 62.5 * 37.5 )

A = sqroot ( 155639648.4375 )

A = 12475.562 m ^ 2

Answer 2

My type mistake.

s = ( 100 + 250 + 275 ) / 2 = 625 / 2 = 312.25 m

Answer 3

Let's scale down the figure by a factor of 25, so it is similar to a triangle with sides 4,10,11

you can use Heron's formula.
sqrt(12.5(12.5-4)(12.5-10)(12.5-11)) ≈ 20

or, you can note that
4^2 = 10^2+11^2-2*10*11*cos(x)
cos(x) = (100+121-16)/220 = 41/44

the area is thus (10*11 sinA)/2 ≈ 20