Area Comparison of Triangles ADE and ABC

An equilateral triangle ABC has a side length of 6 cm. Point D is the midpoint of side BC, and point E is the point on side AC such that DE is perpendicular to AC. Calculate the area of triangle ADE and compare it to the area of triangle ABC.

For the area of triangle ABC, use the formula:

$Area = \f\frac{1}{2} \cdot base \cdot height$

Given the nature of triangle ABC, you’ll also need to find the height from vertex A to side BC. In an equilateral triangle, this can be calculated using:

$height = \f\frac{\sqrt{3}}{2} \cdot side$