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
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
My type mistake.
s = ( 100 + 250 + 275 ) / 2 = 625 / 2 = 312.25 m
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
To find the area of a triangular play area, you can use Heron's formula. Heron's formula states that the area of a triangle with side lengths a, b, and c can be calculated using the semi-perimeter (s) and the formula:
Area = √(s(s-a)(s-b)(s-c))
where s = (a + b + c) / 2.
Let's apply this to find the area of the triangular play area with side lengths 100 m, 250 m, and 275 m.
Step 1: Calculate the semi-perimeter (s):
s = (100 + 250 + 275) / 2 = 625 / 2 = 312.5
Step 2: Calculate the area using Heron's formula:
Area = √(312.5(312.5 - 100)(312.5 - 250)(312.5 - 275))
Simplifying this equation gives:
Area = √(312.5 * 212.5 * 62.5 * 37.5)
Using a calculator, compute the product under the square root:
Area ≈ √(apprx. 859.375 * 62.5 * 37.5)
≈ √(apprx. 21,484.375 * 2343.75)
≈ √(approx. 50,354,492.19)
≈ 7,096.03 m^2
Therefore, the area of the triangular play area is approximately 7,096.03 square meters.