The lateral side of an isosceles triangle is 13 cm, and the half of the base is 5 cm. What is the area of such a triangle?

It follows from the condition that the base is 5 cm x 2 = 10 cm.

Then the area of an isosceles triangle is found by the following formula:

S = (b√a ^ 2 – b ^ 2/4) / 2,

Where:

S – area;

a – side of an isosceles triangle;

b – base of an isosceles triangle.

S = (10√13 ^ 2 – 10 ^ 2/4) / 2 = (10√169 – 100/4) / 2 = (10√169 – 25) / 2 = (10√144) / 2 = 10 x 12/2 = 120/2 = 60 cm2.