Isosceles triangle. The side is 8, the base is 4. Find the area.

Let’s build the height of the ВH of an isosceles triangle on the base of the AC.

The height of an isosceles triangle, drawn to the base, is also its median.

Then AH = CH = AC / 2 = 4/2 = 2 cm, and triangle ABН is rectangular.

In a right-angled triangle ABН, according to the Pythagorean theorem, we determine the length of the BН leg.

BH ^ 2 = AB ^ 2 – AH ^ 2 = 64 – 4 = 60.

BH = 2 * √15 cm.

Determine the area of the triangle ABC.

Savs = AC * ВН / 2 = 4 * 2 * √15 / 2 = 4 * √15 cm2.

Answer: The area of the triangle is 4 * √15 cm2.