The perimeter of an isosceles triangle is 36 and the base is 16. 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.

In order to find the length of the side you need:

AB = BC = (P – AC) / 2;

AB = BC = (36 – 16) / 2 = 20/2 = 10 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 = 36/2 = 18;

S = √ (18 ∙ (18 – 10) ∙ (18 – 10) ∙ (18 – 16)) = √ (18 8 8 2) = √2304 = 48 cm2.

Answer: the area of ​​the triangle is 48 cm2.