The perimeter of an isosceles triangle is 16 and the base is 6, find the area of the triangle.

Let’s designate the triangle as MKL. KL is the base.
Find the sum of the lengths of the sides: MK + ML = 16 – 6 = 10
One side length (MK or ML): 10: 2 = 5

The area of a triangle is found by the formula: S = 1/2 * a * h, where a is the base, h is the height

Let’s denote the height of the triangle as MN and find it:

1) KN = NL = 6: 2 = 3 (since the triangle is isosceles)
2) MN = √ (MK² – KN²) = √ (5² – 3²) = 4 (by the Pythagorean theorem)
Let’s calculate the area:
S = 1/2 * 6 * 4 = 12

Answer: the area of the triangle is 12