### Home > PC > Chapter 2 > Lesson 2.3.2 > Problem2-86

2-86.

Using exact values, find the area of an equilateral triangle with side length $12$ cm.

Sketch an equilateral triangle. Label the angles and sides.

Drop a perpendicular height from $C$ to the base $AB$.

What kind of a triangle is $ΔCDB$?

How long is $DB$?

Using the Pythagorean Theorem, find the height '$h$'.

$30°\text{-}60°\text{-}90°$ triangle

$6 \; \text{cm}$.

Finally, find the area of the triangle multiplying half the height times the base.