# The perimeter of an isosceles triangle is 16 and the lateral side is 5. Find the area of the triangle.

August 23, 2021 | education

| It is known that the perimeter of a triangle (P) is equal to the sum of the lengths of its sides:

P = a + b + c, where a, b, c are the sides of the triangle.

Since the sides are equal in an isosceles triangle, the perimeter of such a triangle will be: P = 2a + c.

If you know the perimeter and side of the triangle, then you can find the third side by the formula:

c = P – 2a,

c = 16 – 2 * 5 = 6 cm.

Let’s calculate the height of the triangle:

h ^ 2 = 5 ^ 2 – 3 ^ 2,

h ^ 2 = 25 – 9,

h ^ 2 = 16,

h = 4.

Let’s calculate the area of the rectangle:

S = 1/2 * c * h,

S = 1/2 * 6 * 4 = 12.

Answer: The area of a given isosceles triangle is 12.