In an isosceles triangle ABC, the height BH = 7 cm is drawn, AB = BC = 12 cm. Calculate the area of the triangle.

First, let’s find the length of the base of the AC of this isosceles triangle.

Consider a right-angled triangle ABН.

Using the Pythagorean theorem, we find | AH |:

| AH | = √ (| AB | ^ 2 – | BH | ^ 2) = √ (12 ^ 2 – 7 ^ 2) = √ (144 – 49) = √95 cm.

Since triangle ABC is isosceles, the height BH drawn to its base is also the median, therefore, | AH | = | HC | and | AC | = 2 * | AH | = 2√95 cm.

Knowing the base and the length of the height drawn to this base, we find the area of the triangle:

7 * 2√95 / 2 = 7√95 cm ^ 2.

Answer: 7√95 cm ^ 2.