The perimeter of an isosceles triangle is 64 and the base is 30. Find the area of the triangle.

An isosceles triangle is a triangle in which two sides are equal and are called lateral sides, and the third unequal is based:
AB = BC.
The perimeter of a triangle is the sum of all its sides:
P = AB + BC + AC;
AB = BC = (P – AC) / 2;
AB = BC = (64 – 30) / 2 = 34/2 = 17 cm.
To calculate the area of ​​a triangle, we will use Heron’s Formula:
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 – 17) ∙ (32 – 17) ∙ (32 – 30)) = √ (32 15 15 ∙ 2) = √14400 = 120 cm2.
Answer: the area of ​​the triangle is 120 cm2.