The perimeter of an isosceles triangle is 32 and the base is 12. Find the area of the triangle.

Given: isosceles triangle ABC;
P avs = 32;
AC = 12;
Find S abc -?
Solution:
1) Consider an isosceles triangle ABC. Lateral sides AB = BC = (32 – 12) / 2 = 20/2 = 10;
2) Let’s draw the height BD. It is also the median. Then AD = DC = 12/2 = 6;
3) Consider a right-angled triangle ABD. By the Pythagorean theorem: BD ^ 2 = AB ^ 2 – AD ^ 2 = 10 ^ 2 – 6 ^ 2 = 100 – 36 = 64; BD = 8;
4) S abc = 1/2 BD * AC;
S abc = 1/2 * 8 * 12;
S abc = (1 * 8 * 12) / 2;
S abc = (1 * 8 * 6) / 1;
S abc = 48.
Answer: 48.