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

March 28, 2021 | education

| 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 = (32 – 12) / 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 = 32/2 = 16 cm;

S = √ (16 ∙ (16 – 10) · (16 – 10) · (16 – 12)) = √ (16 ∙ 6 ∙ 6 ∙ 4) = √2304 = 48 cm2.

Answer: the area of the triangle is 48 cm2.

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