CPM Homework Help : PC Problem 2-86

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

Step 1:

Sketch an equilateral triangle. Label the angles and sides.

Step 2:

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

Step 3:

What kind of a triangle is $ΔCDB$ ?

Step 4:

How long is $DB$ ?

Step 5:

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

Answer 1:

$30°\text{-}60°\text{-}90°$ triangle

Answer 2:

$6 \; \text{cm}$ .

Step 6:

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