find the area of an eqilateral triangle with perimeter 45m
3*side length = 45m
each side = 45/3 = 15m
Height
= 15m * sin(60°)
= 15*(√3)/2
= 7.5√3
Area
= 15m*7.5√3 /2 m
= (225/4)√3 m²
To find the area of an equilateral triangle given its perimeter, we first need to determine the length of each side.
Since an equilateral triangle has three equal sides, we can divide the perimeter by 3 to find the length of each side:
Side length = Perimeter / 3 = 45m / 3 = 15m
Once we have the length of one side, we can use the formula for the area of an equilateral triangle:
Area = (√3 / 4) * (Side length)^2
Plugging in the value of the side length, we get:
Area = (√3 / 4) * (15m)^2
Calculating this expression, we find:
Area = (√3 / 4) * 225m^2
To simplify further, we can multiply (√3 / 4) by 225:
Area = 0.433 * 225m^2
Finally, we can calculate the area of the equilateral triangle:
Area ≈ 97.43m^2
Therefore, the area of the equilateral triangle with a perimeter of 45m is approximately 97.43 square meters.