The length of the lateral side of an isosceles triangle is 5 cm, and its base is 1 cm longer. What is the area of a triangle?

The area of a triangle is equal to the half-product of the base and the height drawn to that base. The height in an isosceles triangle is both a bisector and a median, therefore it divides an isosceles triangle into two identical right-angled triangles.
Base of an isosceles triangle:
5 + 1 = 6 cm.
Leg of a right triangle:
6/2 = 3 cm.
Find the height of an isosceles triangle using the Pythagorean theorem:
a² + b² = c²;
a² + 3² = 5²;
a² + 9 = 25;
a² = 16;
a = 4 cm is the height of an isosceles triangle.
Find the area:
S = 1/2 * 4 * 6 = 12 cm²
Answer: 12 cm²