Question

calculate the area and height of an equilateral triangle whose perimeter is 60 cm

Answer 1

Here
a+b+c=60
Area =bh/2

Answer 2

Well if the perimeter is 60cm and all sides are equal then each side is 20cm.

This would mean that a line representing the height of the triangle will bisect the far side, giving us 2 triangles with 20cm hypotenuses and one side of 10cm and 1 shared side representing the height.

So, 

H² = B² + P²
(20)² = (10)² + P²
400 = 100 + P²
400-100 = P²
300 = P²
P = √300
P = 17.32cm

Area = Base x Height / 2
         = 20cm x 17.30cm
         = 346.4 cm²