Calculate the area of an isosceles triangle if the lateral side is 5 cm and the base is 6 cm.

1. Vertices of a given triangle A, B, C. AB = 5 centimeters (lateral side).

AC = 6 centimeters (base).

2. From the top B we draw the height BE.

3. The height in an isosceles triangle, according to its properties, also serves as a median, that is, it divides the AC side into two identical segments AE and CE.

Therefore AE = CE = AC: 2 = 6: 2 = 3 centimeters.

4. Find the length BE:

BE = √AB² – AE² = √5² – 3² = √16 = 4 centimeters.

5. Calculate the area (S) of the triangle ABC:

S = AC x BE / 2 = 6 x 4/2 = 12 centimeters².

Answer: The area of triangle ABC is 12 centimeters².