Question

calculate the area and perimeter of an equilateral triangle with height of root of six leaving your answers in the surd form

Answer 1

You should make a point to memorize the ratio of sides of the 30-60-90° triangle, which is
1 : √3 : 2

so for yours:
√3/1 = √6/x
√3x = √6
x = √2
then the hypotenuse = 2√2

area = (1/2)base x height =(1/2)(√2)(√6)
= (1/2)√12
= (1/2)2√3
= √3

perimeter = √2 + √6 + 2√2
= 3√2 + √6