In a triangle CDE CD = 1, DE = 2√6, EC = 5. Find the height drawn from the apex of the largest angle of the triangle.

In the triangle CDE, the Pythagorean theorem works.

CE ^ 2 = CD ^ 2 + DE ^ 2.

25 = 1 + 24.

25 = 25.

Then the triangle CDE is rectangular with legs CD = 1 cm, DE = 2 * √6 cm.

The area of the triangle CDE is equal to: Sde = CD * DE / 2 = 1 * 2 * √6 / 2 = √6 cm.

DN is the height of the triangle CDE, then its area will also be equal to:

Sсde = CE * DH / 2.

DN = 2 * Ssde / CE = 2 * √6 / 5 cm.

Answer: The area of the triangle CDE is 2 * √6 / 5 cm.