Find the area of an isosceles triangle with sides 10 cm, 10 cm, and 12 cm.

Given:
isosceles triangle ABC,
AB = BC = 10 centimeters,
AC = 12 centimeters.
Find the area of the triangle ABC, that is, Sавс -?
1) Consider an isosceles triangle ABC. Let’s draw the height of the VN. It is also the median. Then An = NS = 12: 2 = 6 (centimeters).
2) Consider a right-angled triangle ABN. Then, by the Pythagorean theorem (the square of the hypotenuse is equal to the sum of the squares of the legs):
AH ^ 2 + BH ^ 2 = AB ^ 2;
BH ^ 2 = AB ^ 2 – AH ^ 2;
BH ^ 2 = 100 – 36;
BH ^ 2 = 64;
BH = 8 centimeters.
2) Savs = 1/2 * VN * AC;
Saus = 1/2 * 8 * 12;
Savs = 4 * 12;
Sас = 48 cm ^ 2
Answer: Saс = 48 cm ^ 2.