Question

What is the area of an equilateral triangle having height of 12 decimeter

Answer 1

The height creates a right-angled triangle with angles of 30° and 60°

so if the base of that triangle is x, then using the ratios of the 30-60-90 triangle,
x/1 = 12/√3
x = 12/√3 or 12/√3 *√3/√3 = 4√3
So the base of the equilateral triangle is 8√3
giving you an area of
(1/2)(8√3)(12) dm^2
= 48√3 dm^2