Find the area of triangle ABC if side AB = BC = 10 and base AC = 12.

Let us draw the height BK in the triangle, which divides the isosceles triangle ABC into two identical right-angled triangles. The height BK divides the base of the AC isosceles triangle in half:

AK = KС = 12/2 = 6;

According to the Pythagorean theorem, in a right-angled triangle, the sum of the squares of the legs is equal to the square of the hypotenuse. Let’s find the unknown leg BK in the right-angled triangle ABK:

BK² + AK² = AB²;

BК² + 6² = 10²;

BК² + 36 = 100;

BК² = 100 – 36;

BК² = 64;

BK = √64;

BK = 8 – the height of the triangle ABC.

The area of ​​a triangle is equal to 1/2 of the product of the side of the triangle and the height drawn to it:

S = 1/2 * h * bh;

S = 1/2 * 8 * 12 = 4 * 12 = 48.

Answer: 48