What is the area of an equilateral triangle of height 20 units?

Step 1: Find the relation between the side and height of the equilateral triangle.
NOTE: If "h" is the height of the equilateral triangle and "a" its side, we have the relationship
h = a * \frac{\sqrt{3}}{2}
a = \frac {h*2}{\sqrt{3}}
Step 2: Find the side of the equilateral triangle by substitute the h value in the formula
a = \frac {20*2}{\sqrt{3}}
a = \frac{40}{\sqrt{3}}
Step 3: Find the area of the equilateral triangle when you know side
Step 1: Set up a area formula of an equilateral triangle.
NOTE: Equilateral triangle all sides are equal.
Area of equilateral triangle = \frac{\sqrt{3}}{4} a^2
Step 2: Plug in the side (a) value in the area of the equilateral
triangle formula
EXAMPLE: Side a = 10 cm
= \frac{\sqrt{3}}{4} a^2
= \frac{\sqrt{3}}{4} (10)^2
Step 3: Do Some calculations for the required area.
EXAMPLE = \frac{\sqrt{3}}{4} (100)
= \sqrt{3}* 25
= 25 \sqrt{3}