The perimeter of an equilateral triangle is 12 ft find the are of the triangle

For a side of length s, the area of an equilateral triangle is

... A = (√3)/4·s²

The perimeter is the sum of the three equal side lengths, so we have

... 12 ft = 3s

... 4 ft = s

Then the area is

... A = (√3)/4·(4 ft)²

... A = 4√3 ft² ≈ 6.928 ft²

7.9m and 4.3°

step-by-step explanation:

let east be +x and north be +y, x = distance * cos θ, y = distance * sin θ  

for 3.5 south, y = -3.5  

for 8.2, x = 8.2 * cos 30 and y = 8.2 * sin 30  

for 15 west, x = -15  

total x = 8.2 * cos 30 – 15 ≈ -7.9  

total y = -3.5 + 8.2 * sin 30 = 0.6  

magnitude = [(8.2 * cos 30 – 15)^2 + 0.6^2)]^0.5  

the magnitude is approximately 7.9 m  

tan θ = y/x = 0.6/-7.9  

the angle is approximately 4.3˚ north of west