Find the area of an isosceles triangle ABC with base AC = 14 cm and perimeter 64 cm.

In an isosceles triangle, the sides are equal:

AB = BC.

The perimeter of a triangle is the sum of the lengths of its sides:

P = AB + BC + AC.

Since the base of the triangle is 14 cm, and the perimeter is 64 cm, then:

AB = BC = (P – AC) / 2;

AB = BC = (64 – 14) / 2 = 50/2 = 25 cm.

Since we know all three sides of this triangle, we will use Heron’s formula to calculate its area:

S = √p (p – a) (p – b) (p – c); Where:

S is the area of ​​the triangle;

p – semi-perimeter (p = P / 2);

a – side AB;

b – aircraft side;

c – speaker side;

p = 64/2 = 32 cm;

S = √32 * (32 – 25) * (32 – 25) * (32 – 14) = √32 * 7 * 7 * 18 = √28224 = 168 cm2.

Answer: the area of ​​the triangle is 168 cm2.