How to find the area of an isosceles triangle if the perimeter is 324 and the base is 160?

An isosceles triangle is a triangle in which the sides are equal, as well as the angles at the base are equal:

AB = BC;

∠А = ∠С.

Since the perimeter of the triangle is 324 cm, and its base is 160 cm, we can find the length of the sides:

P = AB + BC + AC;

AB = BC = (P – AC) / 2;

AB = BC = (324 – 160) / 2 = 164/2 = 82 cm.

To calculate the area of a triangle, apply Heron’s formula:

S = √p (p – a) (p – b) (p – c);

p = (AB + BC + AC) / 2;

p = (82 + 82 + 160) / 2 = 162 cm.

S = √162 (162 – 82) (162 – 82) (162 – 160) = √162 80 80 2 = √2073600 = 1440 cm2.

Answer: the area of the triangle is 1440 cm2.