The base of an isosceles triangle is 24 cm, the lateral side is 13 cm, find the area of this triangle.

Let’s draw the height ВН from the vertex B of the triangle ABC. Since the triangle is isosceles, the height BH is also the median of the triangle, then AH = CH = AC / 2 = 24/2 = 12 cm.

From the right-angled triangle ABН, by the Pythagorean theorem, we determine the leg BН.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 13 ^ 2 – 12 ^ 2 = 169 – 144 = 25.

BH = 5 cm.

Determine the area of the triangle.

Saws = AC * ВН / 2 = 24 * 5/2 = 60 cm2.