A childrens play area is triangular. The sides of the play area measure 90m ,225m and 255m respectively . Calculate the area of the play area?

thanx

Why did the triangle go to the circus? Because it wanted to join the play area fun! Okay, let's get to the point. To calculate the area of a triangle, we can use Heron's formula. Let's call the sides of the triangle a = 90m, b = 225m, and c = 255m. The semi-perimeter (s) of the triangle is calculated by adding all the sides and dividing by 2: s = (a + b + c) / 2. Once we have the semi-perimeter, we can use Heron's formula:

Area = sqrt(s * (s - a) * (s - b) * (s - c))
Now, let's plug in the values and crunch the numbers. Are you ready? Let's calculate the area of the play area triangle!

To calculate the area of a triangular play area, we can use Heron's formula, which states that the area of a triangle can be found when you know the lengths of all three sides.

Heron's formula:
Area = √(s(s-a)(s-b)(s-c))

where "a," "b," and "c" are the lengths of the sides, and "s" is the semi-perimeter (half the perimeter) of the triangle.

In this case, the lengths of the sides are:
a = 90m
b = 225m
c = 255m

To find the semi-perimeter (s), we can use the formula:
s = (a + b + c) / 2

Now, substitute the values into the formula:
s = (90 + 225 + 255) / 2 = 570 /2 = 285.

Now, plug the values of a, b, c, and s into Heron's formula:
Area = √(285(285-90)(285-225)(285-255))

Perform the calculations inside the parentheses:
Area = √(285 * 195 * 60 * 30)

Multiply the values in the parentheses:
Area = √(3172500 * 1800)

Now, find the square root:
Area = √(5710500000)

Finally, calculate the square root using a calculator or mathematical software:
Area ≈ 75554.53 square meters.

Therefore, the area of the triangular play area is approximately 75554.53 square meters.

Correction: Used Law of cosines to find

one of the angles.

Use Law of Cosines to find one of the

sides:

a = 90 m.
b = 225 m.
c = 255 m.

CosB = (a^2+c^2-b^2)/2ac
CosB=(8100+65025-50625) / 45900=0.4902
B = 60.6 Deg.

Area = 0.5ac*sinB
Area = 0.5*90*255*sin60.6 = 10,000 m^2.